Personally I wouldn't go to India just for one week. It's the kind of place where it's a lot of hassle travelling round, but each place you want to go to, you want to stay in like forever.
I went to:
Delhi - Big, totally crazy, with some stunning British colonial architecture. A nice starting point, especially as the ride from the airport goes through some of the nicer areas (unlike Bombay which apparently goes past loads of slums)
Hardwar - I taught here for 3 months. The Blackpool of India, it's a Hindu sacred place, and very very very very cheesy.
Rishikesh - this was a 25 km bike ride from Hardwar, so I bombed it up there and back quite often (I was somewhat thinner in those days
). Quite a beautiful setting on a relatively sedate bit of the Ganges just at the foothills of the Himalaya. The river has sandy beaches along it which were quite pleasant to just sit and relax
Dehra Dun - not much to see here, just had some friends there.
Mussoorie - old UK Hill station, really beautiful. Stunning mountain views. Quaint decaying old colonial hotels, etc.
Almora - the only hill station not to be built by the British (it was a Moghul hangout), also very very lovely.
Agra - the Taj is beautiful, as is the view from the Red Fort, but as a place it didn't grab me as much as smoe of the other places I visited in India, once you've got those two sights out of the way.
Jaipur - the gateway city to the more deserty areas around Rajasthan. Quite interesting, and of course has the Palace of the Winds (although it's just a facade really). I had one of the best veggie meals of the trip at the hostel I stayed at here, up on the roof. It cost about 50p and was fantastic.
more later.