I used 10001 as a zip and there are quite a few. Obviously could be different based on actual NY location, but I'd imagine they are widely available in NY. I did this about a month ago and it was done right at the drive up window. I scheduled then went at the approximate time and used the drive up. They confirmed my info, passed me a paper bag with the kit and gave me the instructions while at the window. Swap, drop in collection box, wipe down box, drive away. Tested on 11/1 and got results on 11/4.
Scheduling the test was a nightmare - they are booking only 3 days out so all were booked. I woke up at like 4 am to use the bathroom and refreshed the tab open to their booking page so I could grab the newly added, next day of scheduling.