Well then I believe you will find 10 days very short. Anyway If you visit towards the north then go and look the natual beauty of Kashmir. And the historical value of Delhi, Lucknow. If you visit the easter side then do visit Meghalaya, and all the waterfalls will amaze you. If you visit the western side then go for Rajasthan, if you visit the southern side then go for entire southern region, you don't wanna miss anything there.