any hiking trip to any destination will fit in your budget with ease.

Mongolia is probably cheapest, but also one of the coldest. Vietnam shouldn't be too expensive if you go there by train and stay in hostels.

Any tropical country will easily fit in your budget, as long as it isn't Singapore, Hong Kong or Taiwan. Those three are expensive. Most of them will be cheaper to travel in than China.

I went to South Korea on my holidays for a week, visit two cities (Seoul and Gyoung ju). Tickets were 2900 kuai and I just spent other 3000 on accomodation/food/travel expenses etc... Of course I stayed in hostels and didn't eat in big western restaurants. I could recommend the places I stayed as they where very very nice and cheap, and the staff very helpfull. I think I could have spent less if I changed money in advance or on a bank over there, I changed it at the airport and the ripped me off.
South Korea is a very nice place, much more relaxing than big Chinese cities. Travelling around is not difficult or expensive if you plan ahead and check websites for the best ways to get to other cities.
Good luck on your trip wherever you decide to go!