Manali in Himachal Pradesh is perfect for a solo budget traveller. I had visited that place as a solo traveller. You can get so many budget hostels there. From there you can opt for various adventure activities or go to trip to Ladakh. Even you can just enjoy watching views, without doing anything.
Being a student to, I have travelled a lot on budget and totally get your point. The place is irrelevant as you can go anywhere. The main cost are transportation, so look for Manali or Dharamshala, which is nearest. Apart from that, in my experience you should stay in hostels which are very cheap and are perfect for students. This way you can save the two biggest cost. In my opinion Mcleodganj, Dharamshala would be a little cheaper than Manali.