Here are some good tailor shop sin HK. Mind you, it won't be cheap cheap suits. If you want a good quality, then go here. If you really want to cheap out and save money (not that its bad to do that) then you can go to Hollywood Shopping Arcade in MK for $500 suits.
Otherwise here:
http://www.jantzentailor.com/
http://www.samstailor.biz/
http://www.raja-fashions.com/
Getting off the rack will cost you more. It won't fit your $350 budget. I know Hugo Boss was having a sale and many of the suits were around $5000HKD so you can do the math on that. Regular prices are roughly $7500.