Namaste Tseuq!
I am travelling to india this november - february myself too, I can't really recommend any places to stay for x-max / new years eve, as it is my first time visiting the country. What I have gathered information about the country at those times of the year of course it will be filled with other tourists/travellers as well, atleast GOA seems to be a very tourist/traveller gathering place in the last few days of the december so it will be packed with other fellow travellers which will be nice if you would like that kind of thing?
Also just did some reading about the Diwali which will be held around mid november which is kinda the "xmas/new year" for hindus. Not sure how is the western way of new year or xmas be held.
What places are you going to visit there? What are you looking for to do at those x-mas/new years eve times?
I am going to stay a few days at Delhi at first then mostlikely start moving towards south as the weather will get a bit chilly at november/december as what I have read about the seasons there.
Goa will be one of my destinations for sure. But I hope it won't be too packed with people as it will get too pricy to get a budget hostel. Incase that happens I will be moving to some smaller town(s) and go with that. Gokarna has been adviced to me to check it out. Also Kerala.