Delhi

Delhi is a major international transit hub for trains, planes and buses as well as a great connection point for domestic destinations within India. It's also a great base for exploration of the famous Hill Stations.

Agra
and the Taj Mahal are a 3-6 hr drive or train ride each way. Roads are not great so be prepared for a long trip, even if it is quoted as being close and quick. Book tickets in the train cars with seats far in advance, and look for the seats put aside especially for tourists. You can also rent a car and driver for the day and shouldn't pay more than ~Rs 5,000 roundtrip if not less. The Taj Mahal is closed on Friday.
Bandhavgarh National Park
and the Bandhavgarh Fort, are the "Tiger Reserve" at M.P. This is a Tiger preservation project and has the highest density of Tigers in India.
Dharamsala
the seat of the Dalai Lama's government in exile, is 10-12 hr to the north. Tickets can be purchased from Main Bazaar Tourist offices, Majnu ka Tilla Tibetan Settlement or the I.S.B.T.
Shimla
the summer capital of British India and the queen of all hill stations in India. It has many scenic and historic locations and is about an 8 hr drive or 10 hr in a bus. A direct flight from Delhi takes just 1 hr to reach Shimla.
Jaipur
and Rajasthan, are reachable by plane or overnight train.
Kathmandu
in neighbouring Nepal is a roughly 36+ hr by coach, or longer but more comfortably on a combination of train and coach.

The holy cities of Haridwar and Rishikesh, in the foothills of the Himalayas, are a 5-6 hr bus or train ride away.

Mussoorie
one of the original British hill stations in India; also known as The Queen of the Hills.
Nainital
another beautiful hill station in the Kumaon hills with the magnificent Naini Lake.
Char Dham
Delhi is the starting point of the famous piligrimage centres Badrinath, the abode of Vishnu, Kedarnath, the abode of Shiva , Gangothri and Yamunothri, the origin of sacres rivers, Ganges and Yamuna respectively

Ride the Maharajas' Express, a luxury train running between Delhi and Mumbai.