Hey! There are a lot of cosy homestays available in Kasauli. Some of them are: Bara Bungalow
Sheetal homestay
StayApart - Nature stay
Kasauli's Bottom
Samarth Kasauli hills homestay
Hill-View 1BR Home Seclude Summer Vine
Pine Winds villa
There are a lot of other options for budget stays for solo travellers, and also recommendations on places to visit, things to do here: https://www.tripoto.com/kasauli
You can also find real account of travellers in 'trips' that can help you plan your trip better! Hope this helps. Happy travelling :)