Chennai, Mumbai and Bangalore are all barking mad, but an assault on the senses you won't easily forget. Calmer and easier on your head are Goa, Pondicherry and Mangalore. There is history at Delhi, the Red Fort. The Taj Mahal is at Agra, The palaces at Mysore are also something else. Don't be afraid to travel by bus ("Volvo") or by train, (you'll even find that hiring a car and driver is a reasonable expense). You'll see things that you never imagined. Be a bit careful what you eat and where you eat it. I've always organised my own trips, have never used a travel agent. (but most of my trips have been on business).
