I've never trained at the NY Aikikai, but as a member of the USAF I'll give you a little to go on.
First, you should be very welcome to train there. Try to arrive early before the class you wish to attend to fill out paperwork (training waiver, etc). USAF dojos usually follow the white/black belt format, such that all kyu ranks where a white belt. So if your dojo has color belts, you may want to leave that behind and pack just a white belt, unless you are yudansha. If you have some proof of rank or federation ID you can bring that, but you shouldn't need to show it.
The NY Aikikai is the home dojo of Yamada Shihan and Sugano Shihan, two of the most respected aikido practitioners in the world, as well as many high ranking sempai. Go train!! You'll have a great time.