When will you be traveling? At most locations in Asia, kiting is seasonal, so your travel itinerary will have to depend on what time of the year that you go.
Mui Ne is one of the few places where you have good chances of being able to kite no matter what month you visit, since it is exposed to both the northeast and the southwest monsoon winds in combination with having large sand dunes that create a sea breeze effect on all sunny days. Besides, Vietnam is a beautiful and interesting country to visit, so Mui Ne should definitely be on your list regardless of when you come!
Taiwan is another place where you have good chances of wind year-round if you are willing to seek out the right beach (but there are no guarantees). Mui Ne and Taiwan are also some of the few places in Asia where you regularly will get strong winds (7-9 meter bowkite territory, although you will generally be all right with a 12 meter kite for at least a few hours on even the windiest day).
Other locations in Asia are more seasonal, and the wind is generally not as strong. You are unlikely to end up using a kite smaller than 12 meter bowkite (or equivalent) at most other places in Asia.
Thailand is a very nice place to visit, but I would not recommend Koh Samui or Pattaya as kite-specific destinations. Sure, you can kite there in the right season, but there are better and more reliable destinations in Thailand for kiting. Specifically, Chumphon and Hua Hin have very nice, wide beaches with fairly consistent winds from November / December through April and would be my top two choices in Thailand if I went primarily for kiting. Phuket is similar to Koh Samui and Pattaya - it will work at times, but is not really ideal. And by the way, since you say that you are looking for culture and not partying, Pattaya is definitely not for you.
Boracay is supposed to be quite nice but I have not been there myself. In terms of other places, it all depends on the season. For example, Bali can be great in June - August, but don't go there in October. And so on. Let me know when you will go and I will try to give you some specific recommendations.
A second, big kite will definitely save some days on all of these locations. If you travel with only a 12 meter bowkite, there will be days when you will not be able to go out, even "in season".