There’s a website for the NYC studio which is different from the onepeloton members website. You can go here to look at the schedule. You'll need to create a new account, add payment information and then buy one or more classes. Cost I believe is $20 for the first class and then $32/class thereafter.
Then you can click on a particular class and you'll see something like the image below. If you see a number, you can click on that bike to reserve it for the class.
A couple more questions, actually. First - is it easy to get into a class you want to attend or do they fill up fast?Second, which bikes are visible to the camera so my friends riding remotely can see me?
1) How hard it is to get into a class depends on the instructor and day/time. You'll be able to see the schedule about two weeks in advance but reservations open up 1 week prior at 12PM EST/9AM PST. If you're visiting from out of town I would set an alarm to book exactly at that time and make sure to have an account set up, class pass purchased, etc.
2) The most visible bikes are 6,7, 5 and 4. 6 is by far the most visible and is the one you see reflected in the mirror to the right of the instructor when watching a class. If you can't get those and want to be visible I would try 18 or 19.
It's a fun experience to visit the studio and I would recommend trying to squeeze it in if you're visiting NYC. As long as the instructors are not doing back to back classes, they will usually pose for a pic a few minutes after the class. Here's a blog post with a ton of good info about the overall experience.