For New year's you can go to Baga beach, Miramar Beach, Agonda Beach, Candolim Beach. Goan red rice, Bebinca, Poee, Sanna are the foods that you should definitely try when in Goa. For stay you can look up for an Airbnb or Zostel, it will be affordable and you can certainly move around according to your comfort.
Hey Sarraf, I'll be traveling to Goa during the mentioned time, so myself and my friends decided to stay at Tito's lane.we booked ourselves a backpacker hostel. we'll be staying there for 5N . day 1: we'll go for a trek to dudhsagar falls, which is a 2hr drive and start exploring flea market. day 2 -day5 explore Goa from South to North. all the beaches and few good Cafe,etc... please do your booking as fast as possible because the price for your accommodation will triple during DEC- JAN.
North goa is for party lovers where south goa is for leisure. If you are party lover then north goa is perfect for you. Baga beach is too crowded so u can choose calangute beach or candolim beach for stay. club cubana is a disc. Its a must visit place. LPK is another disc which is also really good.u can visit here also but tito's is waste of time.
you can spend ur one evening in Deltin royale cruise where u get some chips with tickegs by which u can play or u can buy more with that buffet n drinks are free with live music. so its a perfect place to spend one evening there.
There is watersports activities too but at this time they may b closed due to rain.
panjim is a good market for shopping. Goa has lots of chruch n fort for explore.
overall goa is best place for tourist where he found everything what he wants.