This addresses two questions about Hammerstein Ballroom.
I'm a New Yorker and have been to several shows there.
Q1. Is there alcohol at the venue?
A1. Yes. I can only speak about the General Admission Floor bars since I've never seen a show from either of the Mezzanines. (I believe the mezzanines have their own bars upstairs.) The bars flank the venue on either side so when you get through the doors to the Floor section you have to move past them to get onto the Floor proper. This means you can hear and basically see the artist while you're in line.
You'll see two long lines by each bar. The disorganized line that extends the width of the bar is in fact the line for the bar. It's not a fun line. Full of shitfaced people trying to cut you. Makes you want to throw elbows. The more or less single-file line near the bar is the bracelet line. Show valid ID proving you're over 21 and you get a bracelet. You can't order at the bar without a bracelet, so don't make the mistake of getting in the bar line first or thinking you can just show the bartender your ID. It won't work and you'll be wasting your time.
***As a sidenote: unsurprisingly, the drinks are somewhat overpriced (although not as overpriced as they are at professional sporting events) and you can easily squander your musical experience waiting in line for booze. Needless to say, the lines are much longer before the show (which will probably be a long time, given Axl's predilection for building audience anticipation) than they are during the performance. However, if you take advantage of the shorter lines during the performance, you're in for a hell of a time (especially at a GN'R show) trying to get back to your place on the floor at all, let alone with your drinks still in their respective cups.
Q2. Can you go up to the Mezzanine with a GA Floor ticket?
A2. Not sure but probably not. They're pretty strict and basically their job is to make sure fire and building codes aren't violated if sections go over-capacity. I imagine given the significance of the shows and GN'R's history of causing serious logistical problems that the security and ticket-taking personel will be especially vigilant and work even harder than usual to enforce the rules-- especially at the first three shows. That said, you'd probably have an easier time using your GA Floor ticket to get to the Mezzanine than you would the other way around, since most people are doing their best to get on the Floor anyway.
Hope this helps a bit.
Have a blast. It's a tiny venue-- minuscule by GN'R standards-- and seeing Axl & Co. there to inaugurate their (TRIUMPHANT) return will be nuts.
Best~