Hi Smit, It depends on where are you traveling from. If you are traveling from Delhi, then you can go North (Himachal Pradesh, Punjab, Uttarakhand) or may be come south of Delhi to Rajasthan.
If you are traveling from Mumbai, then you can go more towards South. Goa is the best budget option. Or you can even go more south to Karnataka ( Coorg, Chikmagaluru, Hampi, Bangalore). Daman is also a good option if you are traveling from Mumbai. Hope that helps!!!
I would suggest that Diu is a great place to travel for a solo traveller. It has beautiful beaches, forts, caves, temples and for those who are interested, booze. The union territory is very well maintained, safe and not crowded at all. Hotels and restaurants are good and affordable. It is well connected with road, rail and air. Law and order situation is very good so suitable for female solo travellers too. It has so many beautiful place which are yet to be explored fully and appreciated. One will instantly feel connected to nature and self once you get here.
OMG! 10k is good amount to travel for week or 10 days I guess. Plenty of places in Himachal Pradesh, Uttar Pradesh, Uttarakhand, Madhya Pradesh and Rajasthan to chose from. You need to be more specific with the region for better help.