Best bet is a hotel. Dont go for the famous named 5 stars they charge a fortune for non-guest. 50-100 per time.

I would go on ctrip and find 4 star chinese hotels near your house. They will tell you if they have a pool and either call them and ask what the price is for non guests or just go and check it out.

Also, some hotels will have monthly passes for gym and pool if you ask.

if you want to spend the money, possible network yourself if your chinese is good, you can get a membership for 7500 at the diplomatic residences near the us embassy, the building with the starbucks and back yard burger has a heated pool and fitness center for the diplomats from around the world, lonely cougar wives are a real threat that could cause some problems but the parties and invites are golden. if your young and hungry, business contacts are everywhere, if your lazy, just enjoy the scenery and the great food in the area.