Virginia Historical Society which includes now the Museum of the Confederacy.
Seven Days Battle (fields)
Yorktown (both ACW and Am Rev significance)
Drury's Bluff
Used to be Tredegar Iron Works, but it's been repurposed to slavery. Nearby is Belle Isle, site of the prison camp.
Virginia State Library - original documents and O.R. Supplemental (plus many, many other works on the ACW).
Bermuda Hundred.
City Point.
Fort Belvoir (and other military forts with good museums)
Other side trips:
Petersburg & the battlefields around it
Overland Campaign battlefields (Wilderness, Spotsylvania CH, North Anna), Cold Harbor (I & II)
Chickahominy
Virginia State Military Museum