Asia is so big and diverse there are so many options when it comes to which are the best. There are so many factors that play into what are the best countries to visit. Do we categorize by cultural experiences? Safety? Cost? Friendliness? Ease of access? Pollution? As there are many different factors there can be no definite answer. If I were to choose my top 5 based on these criteria I would probably rank them:

1. Taiwan: I am a woman who travels alone a good 95% of my time. I chose Taiwan on a whim after dating a Taiwanese man for 2 years. As a woman, Taiwan was EXTREMELY safe, I could travel alone throughout major cities with a friend or by myself without any issues at all, even at 4 AM (while a little tipsy)! In terms of cost, Taiwan is a fairly cheap country with few places really driving up the price. At bars, you usually pay an entrance fee but will get alcohol for free once inside (If it’s a Wednesday night it’s usually ladies night so free entrance and alcohol). A hotel room (not even a hostel!) will set you back only $30 in a major city. A meal will only be a few dollars, I never paid more than $5 for any singular food item while there and even got a few discounts for being a sweaty American woman (just kidding, but I did get a free mango). The people in Taiwan were extremely friendly, they operate on a lot of traditional customs and mannerisms that make their hospitality on point! When I was lost in Tainan, a man offered to drive me to where I was going (he literally went and got his car because I couldn’t figure out the bus system) just because I couldn’t read Chinese on a bus poster. This leads to my final point, ease of access, Taiwan while still a developing country has some of the fastest and most efficient transit systems in the entire world, you can pay only $30 US and go from one end of the country to another in less than 2 hours on the High Speed Rail. The Taipei metro system is one of the cheapest and most accessible in the world, where they even recycle single ride passes! A trip only costs a dollar and some change and you can go so far on that!
2. South Korea: My heart is still in South Korea. While it’s my favorite country that I’ve visited it just doesn’t make the top of my list for a few reasons. For one, while it’s cheap there are certain things that are way more expensive there than in the USA. You can definitely do things cheaply there if you stay in a hostel, but a private room in an AirBNB or a hotel will run you more than Taiwan. If you’re feeling a bit more adventurous you can stay as a solo person in a love motel (they’re actually pretty clean!). Their subway system is quite advanced and it’s very cheap (around $1.5 per ride no matter the distance within the city which is very cheap by American standards). The only issue with their public transit is the cards that you use have to be refilled in cash unless you have a Korean bank account and cash can be hard to come by as the ATMs are scarce for visitors. Entertainment wise there is SO much to do in Seoul alone that you’ll never be bored. They have everything from museums filled with optical illusions to tandem biking down the Han River, there’s something for everything. They have a HUGE cafe culture there that is a treat as the cafe culture has created some unique cafes such as the LEGO cafe, comic book cafes, flower boy cafes, and even raccoon cafes among other unique places. The best part of all of this is the cafe culture and food culture has made food so cheap that it doesn’t make sense NOT to eat out! I personally had so much fun in South Korea that if I had the chance I would move there. Safetywise I always felt safe but you need to be careful if you’re approached by people as South Korea has a lot of cult members who are recruiting on the streets. [1]
3. Japan: I personally have not been to Japan but they are ranked as one of the safest countries in the world. Their violent death rates due to guns are under 10 per year! However, they do have a high suicide rate due to societal pressures. Out of all of these, Japan is one of the most expensive countries according to my friends who have gone, this is in part due to the cost of food and other things, but should not deter you from going. Their transportation system is the most advanced in the world and it shows! You can do so much in Japan and there’s always something going on. I would say that by going to Japan you won’t be disappointed.
4. The Philippines: The Philippines is one of the cheapest Asian countries to visit and one of the most gorgeous. I haven’t been but there will be a day when I finally get the chance to go. You can’t go wrong with the country with the friendliest locals you’ll ever meet.
5. Singapore: One of the most expensive cities in the world (and home to the Crazy, Rich Asians), Singapore is absolutely stunning and filled with unique things to do, Chiangyi Airport alone has a butterfly garden, movie theater and other amazing amenities. Singapore is famous for it’s hawker centers and food as it’s a culturally diverse country filled with all sorts of ethnicities.

Last year I was given the opportunity to visit the city of Tainan in southern Taiwan. Tainan was the original capital of Taiwan before the growth of Taipei and has been a food and cultural epicenter ever since. 
Settled in the 1600s by the Dutch, Tainan city's architecture is a mix of Dutch, Japanese, and traditional Chinese, with buildings dating back to the 1600s varying in style. Because of it's unique heritage, the city boasts everything from sprawling European style buildings to traditional Japanese hotels and everything in between. This rich history has added to a astounding amount of historic sites that tourists can visit, but many do not. 
One of Tainan's best kept secrets is the Anping Treehouse behind the Tait and Co. building in the Anping district of Tainan. Named for the district it's in and for the living banyan tree that occupies the space, this Treehouse is a beautiful reminder of how nature always wins. Originally, the treehouse was a warehouse for a merchantile company called, you guessed it, Tait and Co. Presently, this building is part of a 3 building museum highlighting the merchant trade in Tainan between the Dutch and Chinese, calligraphy and other rotating exhibits. At this time, most of the walls are covered in thick tree branches and roots that give the treehouse it's name. Tourists do have safe, secure walkways that they can use while visiting this attraction.

When we first travel somewhere new we can encounter issues that we are not used to. Things like the heat and humidity, hygiene and just plain cultural differences. Below are my top 5 biggest lessons I learned while in Asia. 

1. No Soap, No TP, No Toilets: Hand Sanitizer, tissues, and bracing for life
One of the biggest issues I found while traveling in Asia is the lack of soap, toilet paper, or "western toilets", things we take for granted in the USA. More often than not, I would find myself in a situation where I only had the option of squatting toilet (a popular choice in Asia). I being the graceful person I am, I would have to brace against the sides of the stall only to find when I was done there was no toilet paper. The best way to solve this is by keeping a pack of travel size tissues in your bag or pocket. When you go to wash your hands if there's not soap, just get some hand sanitizer, it works well in a pinch and will substitute soap. 

2. Your International Debit Card DOESN'T WORK: find a Citibank branch or 7-11
For some reason, some ATMs in public areas do not accept foreign cards, even the ones in popular tourist shopping destination. This can be a major issue if you're in a country with a cash-based economy. For the most part, I was able to always find an ATM that took my card, but there were times where I struggled with getting money, such as places like Songshan Cultural Park which only had ATMs for Taiwanese and Chinese consumers. If you wanted to skip these issues for the most part, the best cards for travel in Asia are Charles Schwabb (USA) and Revolut (Europe/USA/Asia) cards, which forgo typical credit card fees and work worldwide. I have a debit card from a small local bank near my house, however, I have met people who swear by these accounts.

3. In Between Lodging and Have Luggage: Use a Luggage Locker
When you're on the go or just in between hotels, carrying luggage from place to place can be a complete drag especially if it's the middle of summer and 100% humidity. You may be backpacking a country or just switching hotels and your check-in is not until 4:00PM. This can be stressful for anyone, however, I've found there is a viable solution. In many regional rail and subway stations there are luggage lockers where you can lock your luggage away for a predetermined amount of time. It may be a small fee, but if you're tired of lugging things around it is a Godsend.
Similarly, many museums have lockers where you can keep your luggage for a refundable fee. In Seoul, South Korea, I found that most museums would charge 250-500 Won, while similarly in Taiwan it was around 10NTD. These fees are under $1 USD and are paid in coins. While museums in the USA have this feature they usually don't have very large lockers, but I've found the ones in Taiwan are quite large and can easily fit a full-sized suitcase or carry on. This is a cheap way to explore a city until your check in time. 

4. Summer Heat is Oppressive and Taking It's Toll: Stay Hydrated, Eat HOT Foods, and PRAY
While this may seem like a no brainer, you would not believe how often I woke up dehydrated after a day out in the sun in Asia. No matter how many bottles of water I drank I was still perpetually dehydrated. I realized later that I was not doing basic things to keep myself from having issues. First, bring a refillable water bottle with you wherever you go. While it may be easier to buy a 50 cent bottle at a 7-11, you will be adding to the crazy amount of plastic waste already in Asia. Instead, there are many public places where you can find a water fountain or water cooler (Most restaurants have one).
Also, if you're someone who wants to stay cool, eating hot food (spice and temperature) is a surefire way to cool you down. While this may seem redundant, you are more likely to sweat more after eating spicy foods, allowing your body to cool itself down faster. This doesn't mean you can't eat cold food, especially when patbingsu or baobing (Korean or Chinese Shaved Ice with fruit) are so delicious in the summer, it just means if you need to cool down fast, add some hot sauce to your lunch or dinner. 

5. Bringing too Much to Carry on Day Trips: Invest in Multi-use Storage and Minimize Heavy Objects
I admit it, I'm a serial overpacker, even on day trips, and when I'm overseas in a place where it's hot, humid, and I can't communicate well I've made some mistakes. One of the biggest mistakes I've made? Carrying guide and language books around on day trips just in case I need them. These items are heavy and don't really help very much when out and about. While you can purchase them prior to a trip, keep them in the hotel, your phone may be a better option with live offline translations et cetera at your fingertips. You can also create offline maps on Maps.me which uses GPS coordinates and no data to track your location. This will significantly lighten your load and make it easier to enjoy your trip, without cumbersome bags. This tip goes for books you read for pleasure, if you can download it to your phone or Kindle it takes up less space and provides some relief. 
Your backpack or purse is your best friend. If you like to bring your camera like I do, I would suggest buying a bag that has a padded section for your camera (Here's my bag). I carry a DSLR for most of my travels and it can be HEAVY, plus all of your day to day travel items are rattling around the bag with it. When I was in Korea, I made the mistake of using a regular purse and putting a smaller camera bag inside of it. By the end of the day my shoulder was covered in red marks from the straps being weighted down with my camera. Travel camera bags are not much more expensive than a backpack or purse, and they have larger straps to distribute the burden. The backpag I use is a GoGroove bag and it was fantastic, compact but really used space well!
If you don't feel like carrying a bag, buy a fanny pack or money belt, this will keep items out of your pockets (and away from any pickpockets) and secure credit cards, passports and phones. I would suggest even investing in one that hangs around your neck instead of going without. 
Finally, you carry a lot in your hands when you travel: maps, phones, the odd beverage or to go food item. If you can find one, purchase a drink holder from a street vendor. These holders have straps that you can slip on your arm and allow you to carry any drink with ease as it frees up your hands. If you're in a country like Korea or Taiwan you will see a lot of these as they are so useful for carry other items as well.