Hey Anitha, You may go to Kerala. It is very beutiful. I visited there last month. You may follow this itinerary: Reach Kochi by train or plane then ->Kochi sight seeing->Road trip from kochi to Munnar->Munnar sight seeing ->Thekkaday->Kumarkaom->From here to Allepay by boat ride.
If looking for trekking, then I will suggest to try Meesapulimala, Skandagiri, Savandurga. If you need peace then do a solo ride to Namdrolling monastery, Coorg and there are other places to visit at Coorg too.
Hey !! Since its your first solo trip , I would suggest Goa.Its absolutely safe and very friendly for female solo trippers' . I would suggest staying in North Goa in a hostel. I preferred to go to a regular and popular destination during my first solo trip. Did the regular things and stayed at crowded, touristy places. This gave me a hang of how I handle solo trips. And then i started exploring offbeat destinations alone. For some well curated experiences in Goa, you can check out this website/app called Triplived https://www.triplived.com/Index#/ .
You will try for hyderabad (telangana tourism) hyderabad is a metrocity composition of Heritage tourism,pillgramage tourism,amusement parks,urban tourism,you can do shopping as well.. charminar
qutub shahi tombs
baradari pilgrimage tourism chilkuri balaji temple
mecca masjid masstourism destination and amusement parks ramoji film city'
hussian sagar lake
tank bund for boating
nehru zoo park telangana tourism also offers different city tours