Mumbai is definitely a sensory experienceÖ Where in Mumbai will you be located for 4 days, and how many days do you have free? If this is your first trip to the city then must-seeís would include : The Gateway of India (next to the Taj Mahal Hotel), Victoria Terminus (gothic building that looks more like a cathedral than a train stationÖ ), Marine Drive (popular promenade stretching from Nariman Point to the foot of Malabar Hill), Haji Aliís Mosque (containing the tomb of Muslim Saint Haji Ali, accessible at low tide), Mahalaxmi Dhobi Ghat (good photo op), Mahalaxmi Temple (located close of Haji Ali). If you have more time, you could visit the Elephanta Island to see the rock-cut temples. Mumbai also has some very good shopping and excellent restaurants. There are high-end malls or markets like Crawford Market where you literally can get anything... If you're adventurous, you might want to try the street food at Bade Miya's, kebabs to die for...
For places to stay in GoaÖ Basically, you need to decide if you want to stay in the north or the south. The south has lots of upmarket, self-contained resorts and thereís less tourist development and is more laid-back. The north has more nightlife and is livelier, although more crowded and noisy. If good food and parties are important, I suggest staying somewhere in the north. Must sees in goa would include: the Fontainhas area of Panjim, west of Ourem Creek (narrow cobbled streets, balconies, old tiled buildings), the whitewashed Church of Immaculate Conception that towers about the main square, Old Goa and the Basilica of Bom Jesus (famous because it contains the mortal remains of St Francis Xavier), Mapusa Friday market is worth a visit, so is the Anjuna Flea Market on Wednesdays.
About renting a scooter, Goaís one of the few places in India where its actually easy, and I think itís a good way to enjoy Goa. There are all kinds of bikes available on rent. Youíll be asked passport details and your hotel details. I suggest wearing a helmet at all times, although the cops usually fine only on the highways. Make sure youíre carrying the required paperwork. The roads are quite good here compared to other parts of India, but you need to exercise caution, especially if you donít have much experience riding motorcycles.