Hey Neelam,
May is a wonderful time to head to the mountains. You can take a trip to Himachal -- check out Bir or Jibhi. Both the destinations are beautiful and not mainstream, so you're sure to have a great time there. In Uttrakhand, I would suggest you visit Mukteshwar or Binsar. The approach is easy and these destinations aren't crowded either.
You can take a bus to these destinations and stay in hostels and homestays to cut down on expenditure.
Hope this was helpful!