As you are in South India.. if your are looking for beach destination then you can visit Goa or Gokarna. For hill station visit ooty, chickmagalur, kerala, munnar...
Hey Prachi, There are two destinations that are best for your budget and also for cool and calmness ... If you are a beach person head to Varkala in Kerala, as it is a perfect place to celebrate New year also .... If you are a mountain person then head to Coorg which is also called as Scotland of South India ... This is also a best place but it's bit main stream compared to Varkala ... For Varkala :- You have a direct flight to Thiruvananthapuram from chennai and you have to board a bus for one hour to reach varkala from Thiruvananthapuram ... Check out my blog here for the things to do in Varkala :- https://www.google.com/amp/s/www.tripoto.com/trip/wandering-in-varkala-597d7e2a90f1f.amp Check out my blog here for the places to see in Coorg and also the itinerary :- https://www.google.com/amp/s/www.tripoto.com/trip/wandering-in-varkala-597d7e2a90f1f.amp So, if you need to sit and relax and enjoy your time head to Varkala and of you wanna roam round and enjoy mountains head to Coorg .... Happy Travelling !!!
Go for Kanyakumari. Trust me the beaches are excellent and the icing on the cake will be Vivekanand Rock memorial. Sunrise is ultimate and drive on the road by the sea beach will be worthy.