The OP wants somewhere to relax. I didn't think Rajasthan was relaxing when I was there right after 9-11, when there were hardly any other travelers around, probably much less relaxing now. There are international flights out of Kochi, so the OP would only need to fly south, not back to Delhi to fly home.

She says she has to return to Delhi at the end of here weeks travel. She will loose two days travelling if she flys up and back and train is out of the question for such a long way.
So five or six days either on the beach in Goa which will not give you any idea about India, or on a houseboat in Kerala.
I'd still go for Rajasthan, and stay in comfortable hotel. If your budget runs to the best hotels, which it seems to do with most of the people who partake in these forums, I would suggest:
day 1. to Agra. Akbar's Mausoleum on the way. Taj in the evening. Stay at AmanVilas.
day 2. Taj in the early morning. Drive to Jaipur, with a stop at Fatepur Sikri. Stay at Samode haveli. ( it has the best pool in Rajasthan) and is a charming.
day 3,4, City palace, Amber Fort and relax by the pool. Samode haveli
day 5,6,7. drive out to Nawalgarh,and explore the small rural villages and see the amazing havelis in the area.
day 8, head back to Delhi with a night or two at Neemrana Fort Palace hotel. Another amazing place to stay with lovely relaxing pool, and a lovely small village below. It is a short drive back to the airport from Neemrana.
That is what I would do!!
Have fun!

Thanks Shj, your suggestion is certainly worth consideration, as is everyone else's.