Mumbai, formerly known as Bombay, is the economic centre of India and a world-city. There are lots of places to visit including the Gateway To India and Bollywood. If you have some money to spend, stay at the Taj Mahal hotel... a place with tradition...
New Delhi is the capital of India and one of the largest cities in the world. The old city is quite picturesque - as is most of India. Unfortunately Delhi is also the most polluted city in the world and not a safe place for women alone at night...
Agra is world-famous for one of the most beautiful buildings in the world: the Taj Mahal. The completely symmetrical Mausoleum is made of white marble with lots and lots of precious stones built in. If in Agra, don´t forget to visit the red fort as well... Or dine on a roof...
Jaipur is capital of Rajasthan. It takes it's nickname, the Pink City, from pink colored buildings incl. Wind Palace. Nearby is the beautiful Amer/Amber fort/palace, that you could enter on the back of an elephant... Delhi, Agra and Jaipur together form the "Golden Triangle".
Kochi (Cochin) is the largest city in Kerala, one of the more modern, most educated states in India. Tourist will like it that most women still wear sarees and punjabis, not jeans. Kathakali dance is interesting, but very very very slow.
Chennai (Madras) is a major city in the South.
Jaisalmer is a desert city with high walls similar to a fortress. The picturesque city will leave a permanent impression on you. From here it is easy to organize a camel trip to the desert. Please be aware of cheaters! Rates charged by hotels for tours can be a multitude of what the actual rate is!!! Hotels and private accommodations do not own camels...
Mysore, also known as Mysuru, is a pleasant city in Southern India with markets and the Sultan´s palace. Mysore is a great stop when visiting Ooty or Goa as well.