The ice cream parlor is independently owned, but the menu on the wall includes "Jamoca Almond Fudge", a trademarked Baskin-Robbins flavor.
From the inside, the ice cream parlor appears to be located on a narrow street directly across from a large building, but exterior establishing shots place it on the corner of a wide, busy intersection.
In the first scene, Greg is polishing the convertible. Even though it's coated with an anti-glare film to minimize light reflections (made even more obvious where it is missing on the shiny part of the hood he's detailing), the stage lights are clearly identifiable on the other body parts of the car.