Mumbai has many things to show you. its a great torist destination from many years.you dont need to worry about anything.
Things you can see in the mumbai:
Gate way of india( no need to elaborate)
C.S.T. station ( old victorian style railway station)
Chatrapati shivaji maharaj museum ( if you like museum then you can spend your whole day in it)
Elephenta caves( an island with old sculpted cave temple)
Sanjay gandhi national park ( for wildlife safari )
Jahangir art gallery [ a small art museum with free entry ( and dont forget to roam around the roads of art museum you will find some good artist ) ]
Any more places to vist.