I wouldn't advise going there in December, at least in going there for what it's renowned for. The main season is July-August and there may also be some potential for great nightlife in June/September. For the rest of the year I'd say it would be rather quiet...which I guess is good for cheap accomodation/secluded beaches - but it will be rather cold for this anyway.
If you are insistant on going, theres 2 main towns in Ibizia - San Antonio, which is more touristy and has more raging Brits
(and more smaller bars/clubs), and Ibiza town, which is more an authentic Spanish type town/city. The superclubs are spread across the island really.
But for celebrating the new year you'd be much better off going to somewhere like Barcelona or Paris. For a more authentic Spanish feel you'd also be better off going to many other towns/cities in the mainland.