Here's when your budget kicks in
if you have a decent budget, you can consider Japan
One of the greatest thing in Japan is that you'd find the place very tidy and neat, there are a lot of amazing things that will blow your minds away, you can see vending machine of any kind of thing that you can imagine. Also the food is one of the most dedicated in the world. But its relatively expensive to travel there.
As for Korea, is also a rich place to visit too, but first you'd have to look up for what you are interested in, otherwise you wouldn't know where to begin or where to go.
If you want to visit China, you wouldn't need as much of money as you do for Japan, of course depending on where are you planning to go, unless you want to stay the most luxurious place in China of course it'd be very expensive, the best thing to do in China is visit all the historic monuments and shop for cheap stuffs, but be careful, there's always risk buying things in China, since if you ever had experiences with Chinese products, there are a lot of "fake" things that are cheap and tricky to you, don't lose your mind when you see something too "cheap to believe". Also be aware of "nice people" trying to sell you or take you to somewhere on the street. Always be careful and stay safe. However visit China could be very fun too.
This is just my opinion, if you really have a good budget, I'd say, once you are planning to visit Asia, go as many places as you can.
Oh you might also consider Taiwan, is small but full of surprises.