Mumbai Navigator from IITB tells you how to get from one place to another in Mumbai, using the local bus and train services. Also has maps. (Here’s the old Mumbai Navigator.)
Alphonso has the full Mumbai local train timetables as pictures.
If you’re looking for street maps, Google Maps has a pretty good street map of Mumbai. But it’s not as good as MapMyIndia, which gives you the driving route from Nariman Point to Bandra for instance.