Radost18, that's fantastic that you'll be able to do a little reconnaissance. At a minimum, try, if you can, to get a bake time. This could be especially difficult for longer bake pizza, but see if you can clock when the pizza goes in the oven and when it comes out.
If you could do that, it would be a huge help in reverse engineering their recipe. If you want to go the extra mile, here are some suggestions.
1. Bring a still camera. Ask their permission if you can take a few photos (for a blog). If they say it's okay, try to discretely take a zoom photo of the:
bags of flour
mixer (if out in the open)
walk-in (if possible)
and anything else that catches your eye, like empty/discarded packaging
2. Bring a video camera. Again, ask their permission. Film a pizza from the point it goes into the oven to when it comes out. Zoom in on as much of the back of the shop as possible, doing a slow pan to get detail.
3. If they sell dough balls, buy one, and, as you're buying the ball, press for fermentation details.
You: Hi, I'd like to buy a dough ball.
Them: Sure thing
You: When was the dough ball made and how long can I refrigerate it?
You: What's the best amount of time to refrigerate? Do you refrigerate the dough in the pizzeria? How long? How long should I bake it for and at what temp? I really love your crust and am trying to match it as close as possible at home.
4. Dumpster Dive
If you can get a chance to see a cheese wrapper, that would help, as would an empty bag of flour. A camera would be nice, but, be careful. If someone sees you taking photos of their trash, they might get a little suspicious.
Befriending an employee can be especially enlightening, but, I've spent some time in Lyndhurst, and I don't see these guys as being real chatty. Not to mention that they're a 'best in state' winner, so they're probably busy most of the time.
Also, use the bathroom. Sometimes you'll catch a glimpse of a storage area on the way to the bathroom.
If all you end up doing is eating a slice of pizza and making observations, then it's not the end of the world, but whatever other data you can acquire would be incredibly helpful.