Park City has a public lot/garage at the transit center one street east of Main; otherwise park your rig in one of the larger commercial lots just North of downtown or at Deer Valley Resort, and take the free town bus to the transit center. Most of the restaurants on Main place outdoor terraces on the curb for Summer dining and some are dog friendly, just walk Main Street until you find a menu that catches your eye. It's hard to have a bad meal anywhere on Main. I know that the deck at Wasatch Brewing at the top of Main allows well behaved dogs.
Cottonwood Heights, Utah
2016 Evo by Forest River T2050 (23')
2014 Toyota Tundra 5.7L V8
Days camped in 2017: 53 (so far!)