Three days is sufficient time to sample the highlights of Mumbai.
Tourism usually starts in Colaba at the southern tip of the city. The video covers the key sights of the Mumbai including India Gate, the Jain temple and Hanging Gardens of Malabar Hill, a Dhobi Ghat (clothes washing), the Ghandi House museum, Dharavi slum, Sanjay Gandhi National Park, the Kanheri caves, and Crawford market.
While not covered in the video, recommended places to eat include Shamiana restaurant in the Taj Mahal Palace Hotel, and the Konkan Cafe at the Vivanta by Taj Hotel.