I personally would just recommend making an appointment. If you called during regular hours and got the machine, chances are someone just missed the phone, and it will be picked up if you call right back. You just have to tell them what you want to watch, day, and they'll tell you if they have times available--you have to go through the shpeel on the phone and/or when you get there. You're supposed to obtain a special NYPL research card, and I'm usually asked to show mine, but I guess strictness in that can vary. If you have to get one, it's easy to get right there at the library.
I mean, I've just always made an appointment, never tried walk-in. To me it just seems more convenient to make an app't, know you're set and such, but if walking in is fairly simple and you prefer that, go for it I guess. Still, in terms of tape availability, it also helps to make an appointment because (someone correct me if I'm wrong) if someone else is watching the tape at the time you want to walk-in, it may be unavailable.
Again, I just think it's much more convenient to make an appointment, but to each his own.
"If there was a Mount Rushmore for Broadway scores, "West Side Story" would be front and center. It snaps, it crackles it pops! It surges with a roar, its energy and sheer life undiminished by the years" - NYPost reviewer Elisabeth Vincentelli