All the clubs have big NYE bashes, but you need to book tickets for them, and they're quite expensive. I think the tube normally runs late, and they put more night buses on in town, but generally, getting home is a bit of a nightmare.
The tube runs to around 4:30am and it is free to travel after 11:45 NYE, it does get rather busy though. Clubs are expensive, i used to pay around £40 just to get in the door, they are good fun though if your young and carefree so i'd say go for it, i remember those days! Can't really recommend anywhere as haven't been out NYE for a couple of years now, sorry.