Jimmy,
If anyone is going to find a cheap area to live in Beijing, it's going to be your lady!! But for some idea on apartment prices, perhaps ask JimB.....
Beijing is North China, and yes it is bloody cold there right now. The tap water is not safe anywhere in China that i know of. The air in Beijing is one of the worst polluted areas in China when the wind is blowing in the right direction ...lol!!!.
Your then wife, will be relatively safe wherever she lives in China, she will take all necessary means, to make sure of that herself.
David.....