Right in town there's nothing I can suggest. But Rt 5 runs north-south just nearby and you have the really pretty town of Heppenheim right there. With two fantastic castles. Go on a Saturday for the market.
And Worms is really close. Not my favorite city but they also have a good Saturday market. And it's the city where the Ring of the Nibelung cycle is centered on. Very popular with the river cruise ships. Usually there's some kind of music fest going on.
Just up the road is Darmstadt, which I prefer. The schloss downtown is a great museum, and the park is excellent. If there's a fest you should go. You're also just a short drive from prime fossil hunting grounds if that's of interest.
You're very close to the site where Patton crossed the Rhine. That's at Nierstein. Go visit the memorial; you'll probably be the only Americans to do so in a month.
Mannheim and Heidelberg are just a short drive south, but just a little longer in the car will get you to Speyer. That's the place to visit. Excellent cathedral, Celtic graves, and the Technical Museum.
Or if you want small, pretty, historic, places, you're just as close to Bad Durkheim, Freinsheim, or Deidesheim; fantastic spots on the wine road. This is wine central for the region, and less commonly visited than the Rhine or Mosel, but you still have good food, half-timbered houses, castles, and some of the best wine you'll ever taste for the money.