You can do a Shimla spiti trip. that needs these much time frame and it's perfect.. about the budget.. it totally depends upon you.. you can rent a car from Delhi to you can travel by hrtc bus..
Hi shobhit, all the places can't be covered in 5-6 days. Instead you can plan your trip to Manali - Kasol - Tosh - Malana. These all places can covered in 5-6 days comfortably.
In Uttarakhand you can go to following places:
1. Chopta
2. Auli
3. Dhanaulti
4. Kanatal
5. Tihri
6. Chamoli
7. Nagtibba
8. Binsar
9. Munsiyari
10. Mukteshwar
11. Mussoorie and Landour
12. Nainital
13. Kausani
In Himachal you can go to following places:
1. Mcleodganj and Triund
2. Manali
3. Shimla, Chail, Kufri and Narkanda
4. Kasol, Tosh and Kheerganga
5. Bir Billing and Barot Valley
6. Parashar
Stay in hostels/zostels for a budget trip
Hi Shobhit
The best here will be visiting spiti valley from shimla, it will take 5 days, its around 400 km.
It won't be possible to visit all these places.