I would start in New Delhi, make a side trip to Agra, then perhaps take a day to Jaipur. You will see some Indian history, architecture, etc.
Originally Posted by
SK AAR
I will be interested in the culture, history, colonial buildings, etc. I will stay in a up-scale/luxury hotel.
Indian hospitality has its reputation, but I don't know that you will learn much about life in India that way. If you limit yourself to those properties, you'll surely miss out on some interesting sites.