(I swear, on the list of "things Indians sweat pretty hard", Switzerland has got to be up there with Volvos. Nainital is I think the third place I've heard described as "little Switzerland".)
Nainital used to be a British hill station, which is to say, rich white people fled to here every year when the weather got hot. It's mainly a few roads around a lake. It's upscale and very nice.
I whiled away a couple days here, although I did spend a lot of that time in Internet cafes trying to figure out the visa/two-month-rule situation. Still, I did take in a couple of the attractions, including boating on the lake and the cable car up to Snow View. From Snow View, appropriately enough, you can see the Himalayas. And shoot BB guns.
It's kinda tacky too, but on the plus side you can explore new worlds of street food including Bhel Puri, roasted peanuts, and "American-style" corn. You can go bowling, listen to a Nepalese rock band on the street, or eat dinner at a Chandni-Chowk-themed restaurant because you already miss Delhi. You can also do some day hiking, horseback riding, pilgrimages, or golf, though I didn't have time to do any of these.