You can plan your stay in Zostel, Moustache or goStops in Rishikesh, and yes Zostel is now also opened in Mussoorie and they call it dreamiest of all, you can check out there latest hostel here: https://youtu.be/29TFVrqyqKA
Mussorie is very commercial place so it depends on what type of cottage you are going to book, and you can find OYO's there, normal hotels will start from 500 rs per night
Yes you can stay in hostel....I prefer hostel than hotel because they are cheap and in budget......
hostels are about 800rs.for one night....
and it is new and amazing experience.....u may meet many other travelers and believe me it is worth ......
u have to book hostel online because in massorie there is very rush........
some famous hostel chain in India are hostel,Indian backpacker etc...u type hostel in Missouri and there u get lot of list......
thank u