Hi Amir, As I see you are from West Bengal I feel for you travelling to any of the southern part of India (specially Goa and kerela)would be an Issue as flight may not be in the budget you mentioned and if you wish to travel by train the trip won't be possible in time span mentioned by you. So you can try: 1. Camping and other activities in Rishikesh 2.Just chill at hill station like Mussoorie or Dhanaulti 3. Visit Chitrakote Waterfalls which are also called Niagara of India I am not sure about connectivity though(22 hour drive)
4.You can Visit beautiful Madhya Pradesh (22 Hour to Gwalior)
5.Visit Beautiful Beaches of Vishakhapatnam(17 hour drive)
6.Nagzira Wildlife Sanctuary, Nagpur (22 hour drive)
7.Visit Beautiful Darjeeling which is around 14 hours drive 8.Go to Varanasi have beautiful sight of ghat of Ganga and Vibrant ganga Aarti(11 hour) I have suggested all by drive as I am not sure about all the mode of transport to each of the places but you can try Road trip too and may be halt in between and see different places around and come back in 3-4 days it should be fun. I hope you enjoy!
Have you ever tried camping? It would be a great experience. Try camping at the hill stations of Kerala. Live close to nature and experience tent stay and all... Try campper.com , I have done camping with them, and that was awesome.