Century Old Openair Laundry
Since British Colonial Authority gave permission to Dhobi, washerman's cast in centre of Bombay, this place is almost unchanged, except introduction of some modern technology which you can find, if you get into maze like work place (with guide please).
You also can see this railwayside location (not riverside!) from the bridge next to Mahalaxmi Western Railway Station.
From British Era
Victorian monuments of British colonial Era occupy big part of Fort area in South Mumbai.
Gateway of India, a landmark of Mumbai, also Rajabai Clock Tower, Bombay Univercity, Bombay Hight Court, Sassoon Libraly etc... highly recommended to join a walking tour with knowledgeble guide.
You are among locals with religious faiths of which one being the most important : Hinduism. There are many Hindu Temples all over the city. You can check out Saint Thomas Cathedral, Mount Mary Church, Jain Temples in Malabar Hill, Haji Ali Mosque, Zoloastrian Fire Temple (not open to non-zoloastrians), and also the Iskcon Temple.
World Heritage Temple
One hour boat trip from Gateway of India will take you to an island with a cave temple which worships Lord Shiva.
Partially damaged by Portuguese who debarked on the island in 16th century, it conserves world helitage temple with original Hindu gods' sculpture.
All Year Round Religious Events
The city is cosmopolitan and has religious festivals round the year. The biggest is Ganesh Chaturthi, which is dedicated to the Elephant headed God. He is worshipped as the remover of obstacles and hardness, and also considered as the god of prosperity. On the last day, the Ganesh statues are carried into Arabian Sea.
Also check Diwali, Desera, and other religious festivals.
The Lunchbox delivery men
Dabbawallahs, lunchbox distributors collect the lunchboxes from houses, eateries to the workplaces daily. Even in very heavy rain or scorching summer, they don't miss out on their daily work.
They are also mentioned in Forbes. English Prince Charles had also visited Dabbawallahs on his Mumbai visit and even he had to fit in with their schedule.
You can see Dabbawallahs in Churchgate Station around 11:30am on weekdays.
Although we can see more and more footballers in Oval Maidan, this is the place you can see full of cricketers everyday but espacially on weekend.
No wonder this sports is the most popular and mobilizes a great number of people during Indian-Pakistan matches in particulary.
Sacred Space in Town
In the southern part of Malabar Hill Peninsula, old Bombay area where lives most wealthy habitants of the city, there exists one of the most oldest Hindu sacred site, known as Banganga Tank.
According to the legend, Lord Rama had shot the arrow in the middle of the Banganga Tank, and the water is flowing since then.
The water which flows is also considered to be the sacred water of Ganges. There are over 100 temples in the surrounding area, big and small.