The Taj is only as good as the pictures of it. If the weather isn't good, it's not even as good as that. Agra was a stinking cesspit when I was there (mid-late nineties). Avoid it if you can!
North India:
Mussourie hill-station - there's a tibetan monastery that has the best view if you walk to the end of ridge.
I hear the camel trek in the Thar desert in Rajasthan is good. I preferred to stay at the fort-palace hotel in Neemrana. Get a tour of the rooms, they're quite something.
Avoid Delhi, it's a kip. If you do go there, don't stay in Paharganj it's an even bigger kip than the rest of the city (even if it is near the train station).
Middle India
Hampi - full of hippie travellers going "wow, isn't this like amazing, I feel so in touch with the culture"
Goa? If you want a beach, go to one of the Costas and save yourself a packet. If there is anywhere you are likely to be mugged in India, it is Goa and it won't be by an Indian. It'll be by some spaced out traveller who's gone native and run out of money.
South India:
Ooty (Udacamundi sp?) - a hill station in the middle of the the southern plain. Very English at one stage, had gone a bit to seed when I was there, but not popular with tourists.
Kerala - the backwater tour
Cochin - worth a look for the river taxis and the traditional fishing.
Trivandrum (Thiravuranthapuram sp?!) has little to recommend it apart from the meeting of the three seas.
Travel by train or if going by plane, get a discover India pass (it'll allow multiple flights), but I would recommend the trains. 2nd class a/c is quite comfortable, if not exactly private.
If you're going south in November, be aware that the southern second monsoon can still be active then and it can get quite wet. It is good fun, though!
PS I was there mid-nineties, so some of my bad impressions of places may have improved in that time!