4 places from my youth in Utah: Snelgroves, Burger Bar in Roy, the Rolling Scone in Provo, Tony's pizza in Ogden
I think the Burger Bar in Roy is still in business. In fact, it has been featured in Guy Fieri's Diners, Drive-ins and Dives.
It looks like Tony's pizza in Ogden is also still in business. I have very fond memories of their pizza when I was a kid. That was 55+ years ago. I have no idea the quality of their pizza now. Amazing that they have been in business for so long.
There was also a drive-in on Riverdale road in Ogden in the 1960s that served hot scones. Yumm!