Absolutely nothing. We go to a house party the night before and get home about 4. I usually prep a lasagne NYE so I don't have to worry about cooking. When kids were small we'd drive into London early to the museums.
We havent got the stamina for new years eve anymore, age has caught up with us. Instead we go out for a lovely lunch at our local pub after a walk with the dog, then relax in front of the fire and tv pm. Incidentally, the pub is always packed new years day, so many other people have the same idea. Our thinking is that we now celebrate new years day, rather than the night before.
It's almost like a Christmas day mark II here. I'm Welsh so we do Calennig, loosely (no knocking on doors singing, not sure my English neighbours would be up for that!). But we exchange a few small gifts in the morning (nothing like the Christmas excess, more like a few books, nice chocolates, bottles of ale etc). Then we open the champagne and get cracking on lunch, which is basically a Christmas dinner. Carols in the background - we celebrate Christmas right up until twelfth night so perfectly acceptable . After lunch it's a lovely slump until board games and a big film in the evening. The whole thing is lovely.
We don't do new year's eve, so it's our big new year celebration. I love that it's like Christmas with much less expense, stress and ridiculously high expectations - very relaxed, very cosy.