The Eiffel Tower is cool because it's nearest all the fireworks and where everyone gathers, but it's also the farthest from any after-midnight partying, which can suck... That and if you're not staying near the Tower, it'll take you forever to get back to where you're staying.
My recommendation is hanging around the Obelisk in the Place de la Concorde, at the eastern end of the Champs Elysees. You'll have a good view of fireworks, plenty of people to party with, and it's closer to any of the post-midnight action going on, whether you're going to a party at a nightclub, a bar, or just hanging out in the streets around Bastille or St. Michel.
A couple of tips: If you do want to go to a nightclub's NYE party, buy your tickets in advance, or you'll never get in. Some hostels will even sell the tickets/wristbands. If you want champagne, buy a bottle or two at least 2 days in advance, or you'll find that every store's been wiped out of their stock by noon on NYE. You can take the metro anywhere for free during extended hours on NYE, but keep in mind that it'll be like taking a Tokyo commuter train after midnight...