Depends on so many things....
if you are a solo traveller, you have plenty of options...
if you are in a company of one or 2, choose nearest destination so that you won't spend more in reaching to and fro ur destination. if you want to visit beaches, it might b cheap in comparison to water or any other sports activity njoy some unexplored place and have fun
For this one need to know where u stay... so that ur expenses on transportation goes less....But a suggestion is wherever you go... Try to go by Train... !! Also share your interest what kind of tourist you are? Whether u love to go to hill stations or religious sites or heritage sites?
Depend on which place you are currently staying, you can easily cover beaches or any fort or do any trekking near by your area. Also, you can go for solo trip to any monuments
Hey, Under 6 thousand is a very tight budget. So you'd have to take into account every logistic like travel, stay, food, shopping and activities. Try to find a place near you and is suited to your taste. Or if you're anywhere near the South, try Coorg for a quick getaway. Or else try Pondicherry-Mahabalipuram. The latter is a tried and tested one. All The Best.
Depends on where you're traveling from
Rishikesh
Punjab
Jaipur
Manali are a few options in the North. kodaikanal
Coorg
gokarna
allepey and Munnar are places in the south for your budget.
Depends where your starting point is...Assuming metro cities: Rishikesh/Shimla from Delhi; Hampi/Coorg from Bangalore; Lavasa from Mumbai/Pune; Darjeeling from Kolkata; Pondicherry from Chennai; Araku Valley near Vizag; Pachmarhi from MP can be some good options.