Cahokia Mounds — the UNESCO-listed pre-Columbian city — is the most rewarding short trip, just 15 minutes east across the river in Illinois. Allow a half day.
Wine country in southeast Missouri's German-settled Hermann and Augusta has solid Norton-grape wineries and small-town main streets, about an hour west. The bluffs along the Mississippi north of St Louis — Pere Marquette State Park on the Illinois side, the Great River Road on the Missouri side — make a scenic full-day drive in autumn. Hannibal, Mark Twain's hometown, is two hours north and worth the visit for the small but well-curated museum complex of his boyhood haunts.