If u want to see mountains and get closer to nature then visit Himachal Pradesh..u will get to know diverse culture and heritage..unique life style..different mountains with air getting cold and thin as u go high..from Kangra to Spiti..all 12 district have different mountain forms nd many more thing , u only need to get out!!!!!
If it is your first time, you should plan to go to Dalhousie (Khajjiar, also known as as Indian Switzerland) and Mcleodganj. Travel less and have more fun!
You have all other options like Shimla, Manali etc but they are over hyped.