Lower East Side Bar - Good for Groups?
Try Magician bar. It's a low key place that's neither a full on dive, or some lounge substituting velvet food rests for stools. I've never seen it super crowded.
Now that would be my standard safe suggestion without knowing a bit more about your looking for. You might try the Thor bar at the Hotel on Rivington, or Stanton Social.
Verlaine is convenient, but you would have to reserve the fur benches in the front of the bar for that to work. They have a good happy hour there, with Lychee martinis.
Back Room is ridiculous with it's secret bar theme, all ruined by club bouncers standing in front of fake book cases, and waitresses in mini skirts with Cali accents BUT they were taking reservations and can handle large parties. Be warned, the teacups they serve drinks in are not only a rip off, but are designed to make your dribble on yourself. Hey, it's an option though! Might be fun for people.
Paladar is supposed to be good for groups, but it's more of a food place,I think.
The Delancey will let you reserve their roof garden (uh, heat lamps maybe?) but it can get miserable and crowded up there, so I wouldn't recommend it really.
Happy Ending might be a really good choice, but bringing a crowd might be tough there since many of the private rooms are buddy sized.
Not to far away, you can look to the East Village Yacht Club for a more mellow room meant to look like a private alumnus lounge or something of that sort.
Max Fish is just a dive bar, with the lights on. It gets a mostly younger crowd, but it's right up the block from your reservation, and it's fine for a bottle of beer. It's one of the rare bars where men out number women.
The downstairs room at Three of Cups, up in the East Village can be good for groups too. Expect it to look like a college bar though.
One unorthodox suggestion would be Congee Village. They have karaoke rooms downstairs that are pretty wild, and their bar seems pretty extensive.
There is a never ending list of interchangeable loungey places in the area, but none of them strike me as good for parties larger then 6.
There's a reason Magician is never crowded - the service there is downright rude! My friends and I left one night because the bartender started yelling at us after we thanked him for checking our IDs (we meant it in a nice way - ie, thanks for thinking that we're young, because we're not! - but clearly he didin't get that despite our telling him that after he started yelling), and the other two times I was there before that, I stood at the bar for a long time while the bartender blatantly ignored me despite the fact that no one else was in there, and then I got rude treatment when I said "excuse me" to get his attention.
re: scarlet starlet
I wouldn't say that's common for Magician bar. I've never seen a male bartender there, for one thing...but I've experienced what you describe of being ignored when trying to order a drink at about 75% of the dive bars in the city. Magician does get crowded on random days, which kind of ruins it for me, but it seemed a pretty safe suggestion for an area that attempts to cater towards very specific scenes.
Lolita bar is another decent place for some basic drinks, if it's still open.
There are lots of good places in the neighborhood, but seeing as how you're going out on NYE, every single bar (and the streets) will be even more crowded than usual (which means it's going to be REALLY REALLY crowded).
That being said, try Verlaine (just down the block, it's on the north side of Rivington b/w Ludlow and Essex). For some reason that place never really got super popular (read: crowded), but there are always people in there, the drinks are good, and the atmosphere is nice.
Also try Jadis, which is a few blocks down Rivington (b/w Eldridge and Forsyth, a little bit west of the popular stretch b/w Allen and Clinton, so it might be a little less chaotic) - it's a French wine bar and they have some nice group seating areas.
Mason Dixon is not exactly good (I'll go all the way to serviceable), but it is big, so your party of 10 would probably be ok. They seem to have some sort of NYE thing going on, but maybe you'll be early enough that you won't have to deal with it.
Fat Baby might suit you as well.