I've always been satisfied with the pizzas at the Pie Factory either downtown or in Muscle Shoals. This is from my last trip.
We just got the Cheese pizza but it was extremely hot and didn't take that long to arrive at the table but we did have enough time to enjoy one of their Caesar salads. You can also see that it was covered in cheese but yes was the New York crust which is a thin crust but over all it was the best tasting pizza we've found in the Shoals area.