Well india is very diverse country culturally and topographcally, which is best time to travel India, is complicated answer. If u want to visit south india which is quite hot and humid, so better to go in winter time, while if u wana travel himachal pradesh it good to go in summer time but overall best month to travel is August, September october these are the month where temperature will be moderate so that u can enjoy ur journey to best
North - Kasol, Rishikesh, Auli, Manali.
North East- Sikkim, Gangtok, Darjeeling, Nagaland.
South - Coimbatore, Ooty, Coorg, Munnar.
East West - Rajasthan, Puri.
Rajasthan is a nice place if you looking to visit some historic forts & monuments and want to see the architecture. People in Rajasthan are sweet and helpful. They respect their guests.