The official GMAT website has a list of what to bring and what not to bring on test day:
https://www.mba.com/the-gmat/test-day/wh ... enter.aspx
This line (which you can get by following one of the links on the above page to a rules and regulations page) should also be helpful:
You will not be allowed to eat, drink, or use tobacco in the testing room-you may store such items in a locker and use them during breaks.
I'd suggest bringing a quick snack like a Clif Bar or a banana or something just to have the option during one of the breaks to get a quick energy boost or settle some stomach rumblings if you need to. You may well not need it, but it's nice to know the option exists. For that reason you may want to bring a bottle of water or a soft drink, too.
Another tip regarding the sterile testing environment - it can be a little intimidating when you go through the palm scan / mug shot / leave everything in your locker procedure, but remember this: they do all of that intentionally to create both an objective, secure scoring system and an air of pressure to see how you'll react to it. Don't be intimidated - like visiting a Haunted House or watching a scary movie, if you know that the whole design is to scare you it's much, much easier to relax. I looked at it this way - if they really had to go to those lengths to intimidate me in order to keep my score down, that just meant that the questions weren't as hard as advertised or I'd score low just because. So actually that nerve-wracking check-in procedure gave me confidence...I felt like I could call the GMAT's bluff!