I do not recommend the Virginia Museum of the Civil War. I spent a morning there. Its focus is much more narrow than the name implies. It is owned by VMI and covers the Battle of New Market (not the whole war) and focuses on VMI and its cadets.
Lexington, where W&L is, has the Stonewall Jackson Museum, as well as a small museum focusing on Robert E Lee at his tomb. Both more interesting than the Va Museum of the Civil War. Lexington is a bit like Nantucket in the Shenandoah Valley (ie beautifully preserved 18th c town in a gorgeous setting). It is about a 15 minute drive from Natural Bridge, which is also worth seeing.