I stayed here last year, very Central and clean, great value
http://www.hotelcauseway.com/, costs about 300-400 rps in a taxi from the airport.
The Gateway is just around the corner and the Taj hotel, good for a day out to Elephanta Island. There are some good bars in the area and plenty of local colour and some great restaurants too.We hired a taxi for about 4 hours costing 400 rps and he took us round quite a few places, Chowpatty(better at night), Malabar hill, towers of silence, Dhobi ghats, Malaxmi racecourse, cricket ground and finished at crawford market.