New Delhi
Delhi is said to be one of the oldest existing cities in the world, with one part of it, known as New Delhi. We will stay in this city for several 7 days, and the public transport system in this city seems good, there are buses, auto-rickshaws, metro trains and taxis.
Check the Auto-rickshaws - no doors here!

We have the same thing in China, it is fun to try!!
Red Fort
The Red Fort (Lal Qila) is one of Delhi’s top tourist sights. A brilliant red sandstone fort built by the Mughal Emperor Shah Jahan (who also built Agra’s Taj Mahal) as his ruling palace.

Humayun’s Tomb
Humayun’s Tomb in south Delhi, near Hazrat Nizamuddin station, is one of Delhi’s three UNESCO World Heritage Sites.

Qutub Minar
This complex in Mehrauli, houses structures dating from the Slave Dynasty (1206-1290) and is designated as a UNESCO World Heritage Site. The gardens are kept in excellent shape, making this a popular relaxation and picnic spot.

Food!!
Chaat
If you want to eat chaat, the North Indian street side snack food, Delhi is the place to be. Delhi has arguably the best street food in India.
Mumbai
Mumbai is different from the rest of India in pretty much the same way that New York City is different from the United States. The pace of life is more hurried.
We only will stay in this city for 3 days, so time is very limited.
The cool thing in this city is we can travel by ferry, check this out.

Colonial buildings
The British built a magnificent city within the walls of Fort St. George. Some fine examples of the Gothic revival, Neo-classical style and Indo-Saracenic style are seen within this area. Worth seeing are the Gateway of India, the CST terminus, and the Police headquarters or generally just take a stroll around South Mumbai.
Beaches
Mumbai has a few beaches, including one in the downtown area. Some comments online said they are not very great…

Food!!!
I did some research, Mumbai has good street food too. Here is the list:
Butter chicken and naan
Kebab rolls
Indian Chinese
As many different kinds of chaat as your stomach can handle
Indian sweets- milky, delicious concoctions (try the kulfi falooda at Badshah’s in Crawford market)
Vada pav (the great Indian veg burger)
South Indian food from an Udupi restaurant
Kingfisher Blue beer
To get a real flavour of what’s unique to Mumbai, you will have to go a little lower down the scale and experience the street food and Irani cafes. Just remember to check whether the place is clean.
Bangalore
For many years, Bangalore was known throughout India as the most green, liberal and forward-thinking city. In recent years, these attributes have propelled Bangalore to the forefront of the high-tech industry boom in India, and it currently ranks as India’s most developed city and one of the world’s fastest growing urban areas.
This city has auto-rickshaw, too.
Iskcon Temple
Temple built on a hillock in Rajajinagar atop scenic surroundings, is a perfect blend of modern technology and spiritual harmony. The huge cultural complex was built to promote vedic culture and spiritual learning, and abounds with shops selling devotional items and souvenirs. It is home of the ‘Hare Rama Hare Krishna’ movement.

Pub
Experience the Bangalore pub scene, mostly around MG Road, Brigade Road, and Church Street.

Food!!!
Bangalore is far from the sea, and as such the quality of seafood can vary. Some of the higher end and popular seafood places manage this well, but foreign travelers may want to tread a bit carefully.
- Yuxiang Gao
References:
http://wikitravel.org/en/Bangalore#Eat
http://wikitravel.org/en/Bangalore
http://wikitravel.org/en/Mumbai
http://wikitravel.org/en/India
http://wikitravel.org/en/Delhi
http://www.food-india.com/
http://www.indianfoodforever.com/
http://www.tourindia.com/