Two days in Mumbai
The following itinerary basically describes two different ways to spend a day in Mumbai. The itinerary for Day 1 is very different from that of Day 2. Thus, if you simply have a single day to spare, it is best to mix-match and merge the two itineraries. This way you'll experience the real feel of Mumbai.
The price estimates provided below take the transportation, admission fees, food and drink into account. However, it does not include accommodation and the transportation cost between your hotel to the first and last attraction.
Equip yourself well with the following list of items. Start early on Day 1, buy them off the sidewalk/local stores and then begin your day.
Day1: Downtown Loop
Skip your hotel breakfast and hit the streets instead. Songs have been written about Bombay's street food, and the hype is justified. Eat a plate of bhelpuri followed by a vada pav, and cool off with a refreshing glass of coconut or mango juice.
Catch a local train heading south to Chhatrapati Shivaji Terminus. Gaze in awe at the red facade, brass grills and the large entrance clock, each a perfect example of Victorian Railway architecture. After that, it's time to head down to Apollo Bunder and watch the pigeons at the Gateway of India, the icon of the city. To do this, it is best to walk south down the Colaba Causeway, shopping as you stroll along. Turn left into Shivaji Marg after a mile and you will see the Gateway after half a mile. If you feel tired along the way, hop onto Bus 2LTD, 22LTD, 43 or 44. Spend the rest of the morning near the Gateway, and have lunch at one of the Taj's restaurants, where you can expect a gourmet experience.
Take Bus 132 or 70 to the Churchgate Station. Visit Mumbai's two cricket stadiums, the Brabourne and the Wankhede, both a stone's throw away. Catch any train from Churchgate station or simply take a cab to hop off at Marine Lines which is the next station from Churchgate. Welcome to Marine Drive, an arc-shaped road that sweeps a promenade running from Malabar Hill to Nariman Point. Cross the road and you'll find yourself at Chowpatty Beach. Lie down in the sand and relax. Take a dunk in the Arabian Sea. If you're bored, stroll around, watching the traffic swirling past, eating your day's second plate of bhelpuri.
As the sun sets, prepare for a short walk around the Kala Ghoda district. If you're not feeling energetic enough to take a bus, opt for a CoolCab, the blue-and-gray air-conditioned taxis. Get off at The Prince of Wales Museum, renowned for its ivory statuettes, Mughal paintings and objets d'art. Don't spend more than an hour here as the museum shuts by 6PM. Note that it is closed on Mondays. After that, hit Mello Road and you will see the magnificent Esplanade Mansion. Turn left and walk past the Old Secretariat and the David Sassoon Library. Follow your route to the University Road using your road map, and visit the Bombay University Fort Campus. If you still have time to spare, you can select any of the following sights. All of them are equally impressive.
Walk further down the causeway and relieve yourself at the famous Leopald's Café. That's it for Day 1. Take a taxi back to your hotel.
Day 2: Beaches, Shopping and more...
Day 2 races you through the attractions that you missed out on Day 1. Approximate cost per person: Rs 500.
Day 2 involves long-distance traveling, so buy a Day Pass if you choose to travel by the red buses. They're cheap, regular and are a fascinating way to travel through the streets of Bombay.
Start off with a light breakfast of pastries and coffee at your local branch of Barista  or Cafe Coffee Day . Make your way to Mumbai Central and walk around Bombay's midtown, an extremely busy neighborhood that is considered the heart of Mumbai.
Another option is a Tour through Dharavi, according to the density the biggest slum in Asia. The Tour is organized by Reality Tours and Travel  and costs RS 500. It starts around 9.15am in Churchgate or 10am at Mahim Station and takes 2,5 to 3 hours. You learn a lot of the economical power and the unique sense of community in Dharavi. 80% of the profits goes to different non-profit projects in Dharavi.
Afternoon and Evening
Choose between two different itineraries, the Shopping Spree or the Beach Chilling.
Bombay is a shopper's paradise. Start off at Kemp's corner, where you could buy some nice old second-hand books and antiques at rock bottom prices. After that, move on to Inorbit  , one of Asia's largest malls, where you can buy trendy upmarket wear, electronics, cosmetics, gifts and books. Eat at any of the 15 restaurants and cafes, or try India's largest food court on the third floor.
Link Road (the same street on which Inorbit is located) has plenty of good shops.
Bombay has plenty of beaches from which to choose. Start off by strolling down the Bandra Promenade, marveling at the promenade. Follow that up with Juhu, famous for its bhelpuri and infamous for the litter strewn all over the area. If you want to see some clean but otherwise pretty boring beaches, go north in a local to the suburbs of Northwest Mumbai and get off at any any of the Western Line stations. Goregaon is another option in the same area, and is home to the Bollywood filmcity.
Once you're done, eat dinner at one of the numerous Udupi restaurants, where you can savor delicious idlis or dosas, served with piping hot sambhar.
Mumbai is a safe city and violent crime is fairly low. However, beware of pickpockets and keep your money safely in your wallet.