I agree with the above advice. Best to stick to one region of India.
If you pick the North, then go to Agra, Jaipur, Udaipur.
If you pick the South, then go to the states of Kerala and TamilNadu (lots of places to see in both).

Also, as someone else suggested, you should get a travel agent who can organize your itinerary in India and also set up hotel/transportation, etc. It will be hard to just go there and wing-it.