There are many motorcycle stores that sell second hand bikes. They buy bikes at a cheaper price, take them apart, clean the insides, replace what is needed, spray them over so they look almost perfect. I bought a 150cc for NT30 000 two years ago and it hasn't given me any problems. I would rather buy a bike from a store, not through a private sale, because stores usually give you free maintenance if anything breaks within the first couple of months.
Once you are here, just walk around local bike shop streets and look for your best deal. Here is a link of what to expect from a store. If you can read Chinese, the yahoo auction website is pretty good for finding exactly what you want. Here are bikes available here. There are also BIGGGGGGGGGGGGGGG bikes, if you're into those I can search around and see if I can find some stores.
http://tw.user.bid.yahoo.com/tw/user/Y6 ... 513175&tp= you can click on the type of bike you like to see the individual bikes they have for sale. I think those mini ones at the top are all new.