Is the pizza at the counter service places pre-made or would it be possible to ask to have a cheese pizza without sauce made for a child that cannot eat tomatoe?
While they are made somewhat in advance, they will make a fresh pizza to accomodate a dietary need. At Pizzafari in AK, I get a pizza with soy cheese b/c of my milk allergy.
I'd check with the restaurant before I'd count on no sauce. It is possible they have pizza's pre-made with soy cheese because dairy intolerances are pretty common. I've never had a counter service pizza that didn't taste frozen to me!