Shenandoah is pretty much the western third of the State. There's a lot to do in the area. The Battlefields Historic Area in Winchester at the top of the state. You can check out George Washington's Offices, the Patsy Cline sites, Stonewall Jackson's Headquarters, the Museum of the Shenandoah in Winchester. The Shenandoah National Park, Front Royal. Thomas Jefferson's Monticello and UVA in Charlottesville. Luray Caverns, Luray. Natural Bridge below Roanoke. Lots of wineries, horseback riding, golfing, White water rafting. about 6 years ago
My wife and I and 7yr old son went in October 2012. In the park, we spent most of the time in the eastern and middle sections. There are lots of great hikes and the Ranger programs were interesting. We also liked the Junior Ranger activities.
Outside of the park, we really liked Luray Caverns (there's also a car museum and a hedge maze there). We also drove a bit west to the natural bridge (Great!) and a drive through zoo (better than expected). We spent a day at Montecello and went to a winery.
As only 2 of our 5 days in the area were spent in the park, we stayed off site to save some money. As a lot of the adventure in the area involves a drive, the extra half hour to get to our hotel was no big deal. I think we stayed in Hendersonville, but any of the towns west of the Park near the freeway would work so long as they're near one of the roads that lead to a park entrance. This also gave us a pool for our son in the evenings and on one rainy day. about 6 years ago