Things not to miss on this itinerary?

I have a rough itinerary that will take me from Bangalore to Shimla in about 4 weeks, in November. Places on the route I plan to stop at for at least 2-3 days include Bangalore (maybe with a day trip to Mysore), Bombay, Ajanta & Ellora, Jaipur, Udaipur, Simla and Delhi.
I have a guidebook and I have read it, but I would like to hear from Indians and India fans alike what they think is unmissable in these places. Also, if you have favorite small museums, restaurants and scenic spots that might not be mentioned in guide books but are worth seeing, as well as local festivals that might be interesting to a foreigner. Any suggestions?

Mysore and Hyderabad are both important places with a lot to see.

Why not fit Hampi in? I would spend more than a day in Mysore and forget Mumbai altogether. It's just not that interesting. You could go from Bangalore to Mysore to Hampi (you'll most likely double back through Bangalore) to Hyderabad to Aurangabad (for Ellora/Ajanta) and onwards from there.
You could do some of this travel at night, if you're pressed for time. Is there any particular reason you have to spend time in Bangalore? Not a very interesting place, in comparison to the others you've selected.

Why not fit in Agra to see 'The Taj' between Jaipur-delhi lag(Jaipur to Agra to Delhi). You will need a day for Agra atleast.

I'm visiting a friend in Bangalore.