Go for the triund trek in McLeod ganj which is just an overnight journey away from delhi. Or you can also go for the Parashar lake trek which is also at almost same distance.
I think you should be doing Parashar Lake trek . It's a few hours of trek and you could stay there for a day and enjoy the nature . All this can be done in the limited time period of yours.
Go for Kedarkantha (12500 ft) or Churdhar 13000ft high. You will enjoy the place. Lovely trekking experience and awesome wheather. Very less people go thr as most of the people don't know these places. You can find campsites also.
You can opt for a trek to Kheerganga, Bir - Biling and Triund in Himachal. Uttarakhand is also a good option, where you can explore places like Mukteshwar (very scenic and beautiful), Chandrashila trek and even Auli is a very good place.