Where are you based? What kind of weather do you normally live in? And what kind of tourism you like?
If you do not live in equatorial regions, North India, though at its coldest, would probably be still fine for you. If you go to hill stations in Himalayas, you'd see snowfall and all. Lot of South and West Indian places would have a fine weather. A place like Chennai would still be hot and humid.
There are plenty of places for cultural as well as natural tourism in India. There are well known tourist places, and some interesting lesser known ones.
If you are up for some cultural tourism, some of the well known touristy places are
North/Central: Delhi, Agra, Jaipur, Lucknow, Rajgir, Varanasi, Khajuraho, Bhubaneshwar
West: Ajanta caves
South: Mahabaleshwar, Hyderabad, Pondicherr and several other places actually