Hi Mate,
I'm in the same position as you. Travelling solo and also a little nervous and will arrive in Sydney a few days before Christmas. I found it an absolute nightmare to find any accommodation that wasn't ridiculously overpriced due to Xmas and NYE, but I ended up getting an okay price to stay at Surfside Bondi Beach backpackers. Had to bite the bullet a bit with the price, but it was between Bondi or staying in Kings Cross and I heard from many people to avoid that area haha.
Have you booked anywhere up yet? And do you have much of a plan for after NYE or you just thinking of winging it? Be good to know as I literally don't really know what to do afterwards!
Cheers,
Liam