Check the following at Kasauli :
Treebo Trip Royal Suites Kasauli
The Royal Orbit
Hotel Whispering Winds
All are nice hotels in peaceful locality and within your budget
You can always visit Nainital uttrakhand you can stay at Sherwani hotel where you will get a luxury stay with a beautiful view as it is situated on the heights of Nainital and away from the main market. Great weather and peace. For any details you can always message me. Thank you.
Hey Pragati, There's a place called @KahalJungle in Nainital, situated in middle of a Jungle. This place is so peaceful that you'll even listen the deer barking at night, and come across milky way juat above your heads at night. Moreover you can see the himalayan ranges from Kahal Jungle and explore the water falls nearby. Google for more details. I'll provide you their contact number if you're interested.