Skinner and Chalmers drive past a Steamed Hams restaurant during their road trip.
The Simpson family only have around two minutes of screen time, and Homer and Marge don't appear until the post-credits scene, a rare instance where the Simpson family only appear in minor roles.
Since Cincinnati is 800 miles from Springfield and the first state they cross into is Missouri, the most likely location of Springfield would be Springfield, Nebraska which is roughly ~750 mi away from Cincinnati.
Skinner's mother's Buick appears to be a 1980s vintage Riviera. The keys are depicted correctly, with an oval for doors and trunk, and a square for the ignition. The judge's Oldsmobile is also 1980s vintage.