Hello Guchhi, i would prefer Shimla and Manali as its more vibrant and you have more things to visit and do here compared to Nainital. As you are going with your school friends its better you visit some vibrant and happening place.
Hi If you have to choose from these 3 then go to Shimla and cover nearby areas- Narkanda, Kufri, Chail, Theog, Mashobra
Other places where you can go:
8. Valley of Flowers
9. Mana Village