This federal Custom House, completed in 1859, was the site of the Wheeling Conventions of 1861 at which Unionist delegates from western Virginia broke away from the Confederate state government in Richmond. The building has been restored to its Civil War-era appearance and operates as a museum covering the formation of West Virginia. Small but genuinely interesting, especially if you're curious about the political mechanics of how a state splits in two during a war.
West Virginia Independence Hall
Birthplace of West Virginia, where secession was rejected
A story
It was in this building, then the U.S. Custom House, that delegates met in 1861 to declare Virginia's secession from the Union illegal and form a loyalist government — the first step toward West Virginia becoming a separate state in 1863. The building is sometimes called the "birthplace of West Virginia."