Try goa,hampi or pondicherry. There are few hostels for solo backpackers in these places which provide budget accomodation and you will get to meet many travellers allover the world and grow your traveller fraternity.Make sure you carry offline maps and let your loved ones know your location and wellbeing frequently.Cheers!!
You can visit pondicherry which is one of the safest places to visit for a female traveler and the climate there is amazing as of now. I had been there for my solo trip. So if you want any details regarding the same, you could message me. For an overview, you could read Mt trip to pondicherry and also see the photoblog .
Its your first solo then you should try the most popular and easy to travel place to build your confidance, you can visit the place where it is normal to travel like goa, kerela, manali ,shimla, mussorie, you can even try nearby area like mountabu (if u love architecture)