Goa is most popular destination in the country. It is blessed with lots of beautiful beaches to explore. It is the place where many folks plan a trip on their holiday to chill-out from regular lifestyle. Awesome beaches in Goa are Palolem, Querim, Arambol, Patnem, Agonda, Anjuna.
You can also have a look of beach resorts in Goa.
https://www.indianeagle.com/traveldiary/beach-resorts-in-south-goa/
If you have time constraints then visit Lansdowne. If you want to experience blissful nature and great hospitality, visit Almora and stay at HOTs Hostel, Kasar Devi. While in Almora, you could also visit Binsar Wildlife (Leopard) Santuary. If you want to have a feeling of 'Ye India Mein Hi Hai Kya?' go on for Pithoragarh, Munsiyari (simultaneously offering you serene & peaceful time) or visit Chopta/Auli.
It depends which area you want to visit. for celebration you can visit mumbai,goa or pondicherry, according to me these are the best places to celebrate new year.
Nainital is closest if you are planning to go to the mountains, other than that banaras, mathura/vrindavan, ayodhya, agra, rishikesh, jim corbett etc are good options. If you can taje one extra day off then there are a lot of other options available