I think Hampi will be best to enjoy at grand. Its safe, cheap, blissful and beautiful. VRL bus available to direct hospet. You can read my blog - https://www.tripoto.com/trip/3-days-in-hampi-with-budget-of-rs2500-5c3f94bfca088 Or Kokan coast is not less than any heaven. They can visit Kashid, Murud, Aare ware, Arvi and shrivardhan beach.
Gokarna is a fantastic place and any place is safe depending on the area you choose to live in and how you choose to interact with the locals. Being a solo female traveller myself, I can tell you that I've been to places like Bali (which are very unsafe) and had safe experiences only by choosing to go to specific areas. Gokarna is a super safe place and it is much safer compared to Goa. There are budget resorts here too which are right on the beach and provide a safe and cheap escapade. Should do Gokarna!
Hi Devaditya, I went on an All girls trip from Bangalore to Pune and it was totally safe. We did one day trips to Lonavala and Mahabaleswar because we wanted to stay in Pune itself.