Navi - cheaper, but very far. Agree with Keyser, avoid.
Andheri - Closer to airport, but far from most things a tourist would likely want to do. More residential, but nearby Juhu and Lokhandwala. Both are nice, but they would be on my "if time" list.
Central Station - Further from airport, but closer to tourist sites than Andheri. Note Central Station is not the same as Victoria Terminus or Churchgate, both of which are further south.
South - Recommended. Lots of great hotels, close to tourist sites (Colaba, Fort, Malabar Hill, Marine Drive, etc.), and filled with more of the traditional Mumbai. However, it is further from the airport and on the more expensive side.