Agra fort is worth the visit, far better than the red fort in Delhi IMO (both worth doing).
In Delhi itself you can spend a good few days. New delhi/ the governement biuldings for some very english archtecture (Lutyens), Old delhi's bustling streets, Chandri Chawk area, the Friday Mosque, the red fort....a trip to the railwaystation to book a train ticket! Don't be a wimp, do it in person...it's part of the Indian experience!
Varanassi for 2 or 3 days, walk the ghats and dip your toe in the Gangees. One of the oldest, still in use, cities in the world. I reckon it is better to visit than Mumbai.
Pick up a rough guide to india, I spent a month out there and found the guide book very wrth while.
Oh and if you can spare the time, Bandhavgar national park, safari, with luck you'll see tigers, its probably the best place to see them but it took a day of travelling - 3 or more changes of trains to get there so a couple of days in the park will need 4 days on your itinerary.
Don't fret about the food and getting delhi belly, like others I lost over a stone in a month but it was worth it for the experience, the barghees, samozas and best of all...Lassi