Mumbai as a city has lot to offer. You can explore gardens, enjoy sea view at marine drive, Aksa and Juhu beaches, eat food and enjoy night life in colaba etc. But if you want to escape the crowd you can visit, Kashid beach, Mahabaleshwar, Matheran. The famous Lonavalaa and Khandala drives from Mumbai to Pune. You can plan your itinerary and see what all places do you wanna explore.
In mumbai you can go to gateway of India,the view of hotel taj and surroundings has good vibe,walk to colaba causeway for very reasonable street shopping..just bargain this the best fashion place with all clothing,jwellery,footwear.
Go to marine drive for the best sunset view of the city and you can spend hours there sitting and watching people.
Go to chowpatty beach to enjoy the local mumbai flavours and beach time.
If you have excess time visit elephanta caves,alibaug beach,Lonavala,Khandala ghats
Mumbai as a destination to travel has many places to explore! The city itself is an experience - fast life, lots of food, drinks and a sea view to experience. But if you are looking at adventure and some outdoor travel we have Alibaug, Matheran, Mahabaleshwar, Lonavala, Khandala, Pune, along with the ranges of Sahyadris which are within the vicinity of 200 - 300 kms from Mumbai.