Wheeling's location in the Northern Panhandle puts several worthwhile destinations within an hour's drive.
Moundsville (15 miles south on US-250) has two unusual attractions: Grave Creek Mound, the largest conical burial mound built by the Adena people, dating to around 250 BC, and the West Virginia Penitentiary, a massive Gothic Revival prison that operated from 1876 to 1995 and now runs tours. The combination of prehistoric earthwork and Victorian prison architecture makes for a strange afternoon.
Homer Laughlin China Factory (East Liverpool, Ohio — about 30 miles northwest) is where Fiesta dinnerware has been made since 1936. Tours of the factory are available and the factory store sells seconds at a discount. Worth a stop if you're a fan of the ware or just curious how industrial ceramics production works.