Buffalo pizza tends to be in the middle in terms of thickness: not deep dish as the pizza from Chicago nor thin like the offerings from New Haven or NYC. If your search is for thin pizza, you may have trouble finding many choices.
One place with decent thin crust pizza is Stevie V's in Lockport. It is not super thin like the pizza I have had in New Haven, but it is very good. Here is a picture of the entire pizza, with mozzarella cheese and pepperoni. The cheese is proportioned well and does not overwhelm the crust.
The flavor is very good, and the crust is pretty crispy, although you won't find many charred edges:
Monday nights they have a special where you pay the price based on the time you call in (from 5:00 PM until 9:00 PM): for example, calling at 5:05 gets you a large pizza for $5.05.
Anyone staying over from the September RF tour or coming in early would do well to give this place a try. No; it won't replicate what you find in New Haven, but it helps to hold me over until the next trip to Connecticut. The staff is unfailing friendly and always make you feel welcome.
The contact information is below:
Stevie V's Pizzeria
6318 Robinson Rd
Lockport, NY 14094