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...
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...
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".
Varanasi (aka. Benares) is one of the oldest living cities in the world! The city is very much alive and the center of the Hindu religion. People come here to pray, to wash in the river Ganges and to get cremated. For tourists this city is a highlight of any visit to India, but please show respect.
Pushkar is a city in Rajasthan, a pilgrimage site for Hindus and Sikhs with a sacred lake and the largest Camel + Elephant market in the world.
Darjeeling is one of the most remote places in the Indian sub-continent, where it is located between Nepal and Bhutan. The area is known for mountains and tea.
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.
Kolkata (Calcutta) is one of the three gigantic cities in India. It is probably the poorest, where riksjas can still be on foot. Mother Theresa lived three for many years to care for a needy population.