Uttarakhand or Himachal Pradesh. Both are stunning.
In Uttarakhand you could go for Dehradun, Rishikesh, Auli or some lesser explored places like Sankri, Govind Ghat, Ghangria.
As for Himachal Pradesh, Manali and Shimla will definitely be beautiful this time of the year. For some off beat locations, you could try Bir Billing, Mckleodganj, Triund Top.
Hey Swechha,
For 5 to 6 days from delhi ...you Visit these Places :-
These are the best you can take :-
The infamous golden triangle trip ...
Delhi Agra Jaipur and back to Delhi
The other one is ...
Delhi Mussoourie Rishikesh Haridwar and then back to Delhi
You can visit Jim Corbett national park with nainital ...
Delhi jaipur Udaipur and then to Mount abu and back to delhi ...
Happy Travelling!!!