Fiji Island hopping over New Yrs

Hi people, my boyfriend and I will be heading to Fiji for about 2 weeks after Christmas (hopefully before if I can convince my family I dont need to see them for xmas). And we want to do a bit of island hopping. We also dont want to go with a tour we dont think as they seem quite expensive.

My first question is, which islands should we visit in the 2 weeks? We want a mixture of everything.. partying, relaxation, diving is a must, lazy white sand beach days. We also definitely want to see the culture, and visit some villages.

My 2nd question is, we want a big new years eve. Whats the best island to have a great new years eve on?

And lastly, anyone recommend cheapish and nice accomodation on these islands?

I'll leave specific recommendations to others {but you should indicate your budget}. I just want to say that the popular places are often full for Christmas and NYE by about September, so try to plan on booking your main places by then.

Beachcomber is a big party place, for one suggestion.