Got both shots of the vaccine at the Meadowlands Megasite. It's the same complex where the NY Giants and NJ Devils play, though the vaccination is done in the race track viewing stadium.
For my first shot, I had to wait in line for over an hour, but for my second shot the line was only 15 minutes. The National Guard is there to help facilitate with the line. They check that you have an appointment when you get in line (the confirmation email is sufficient). My temperature was checked when I reached the entrance of the building, and they also checked ID and lookup your appointment info on a computer. If it's your first shot, then you wait in a short line to make your second appointment before getting the shot. Afterwards, there's a voluntary 15 minute waiting area in case you have serious side effects such as difficulty breathing, etc.
I didn't suffer any major side effects. For my first shot, I initially just had a very sore arm. After serveral hours, I had a slight headache and was very tired and ended up sleeping for 12 hours and felt fine after that, except for the sore arm which lasted another day. For my second shot, I had not side effects besides a sore arm.
Those in NJ can follow @C19VaxxUpdates on twitter for updates on the latest vaccine availability in the state (though by the time I post this, vaccines will probably be more easily available)