Nainital is a popular hill station of India, a summer spot where camping is a must to do. Will share one Tripoto article written by a traveller pertaining to camping in Nainital. See if it is suitable for your travel. https://www.tripoto.com/india/trips/weekend-camping-in-camp-kuria-nainital-5bb1e7bfe3fff Here are some more camping sites you might try exploring. Camp Kuria a nature spot Wildland camping site
Dolmaar riverside camping
Camp Corbett Hidden valley camp