Finding decent, affordable housing in Mumbai as an expat is like hunting for buried treasure without a map.
The real estate market in Mumbai grew by leaps and bounds in the early 2000s, finally slowing down in 2008. Prices are still high, though - an acceptable three bedroom apartment in a new building located in central Mumbai can easily cost $6,000.00 USD a month, and that's not including the ridiculously expensive utility bills that come with it. As the global recession slowly improves, real estate is likely to rise again. A word to the wise - negotiate a hefty housing allowance as part of your contract.
Most expats live in newer high-rise apartment buildings. There are some bungalow style "houses," but most are old and rundown, making the many new apartment buildings sprouting around the city more attractive. You will want to consider location as one of the most important factors, above the rare pool or gym some buildings have. Because Mumbai traffic is astoundingly heavy, distances are longer than they look. Choose something close to important places such as work, schools, and shopping.
Keep in mind that Indian standards of quality do not compare to Western standards. More often than not, quality does not correlate with price at all. This can make apartment hunting time consuming and aggravating. Give yourself ample time to find your Mumbai home and don't do it on your own. It is an absolute necessity to have several trustworthy real estate agents helping you track down accommodation. Be very clear and firm about what you are looking for, and avoid stating your budget at the outset.
Just like everything else in Mumbai, prices are negotiable. Remember that to Indians, being a foreigner means you must be rich, and you will be charged accordingly. If you state what your price range is right from the beggining, any and all apartments shown to you regardless of size, location, or quality will be right at your max budget - obviously the realtor hopes you will settle for an apartment at an inflated price. Be careful.
Many apartment owners will wait until they find a tenant before renovating, so when you are in the negotiation stage, make a list of requirements from repainting the walls, to refitting the bathrooms, to installing appliances and curtains. Many repairs and requests can be fulfilled as part of the rental agreement. It is a good idea to postpone moving in and paying rent until the work is completed so the owner is motivated to complete all renovations and installations.