Shenandoah National Park is nearby. Skyline Drive/Blue Ridge Parkway is nice, especially if you're from the midwest (it won't compete with the western mountains ranges/parks). Humpback Rock is my favorite of the hikes that's close to the I-64 access to the park. Stop at Blue Mountain Brewery on the way back, they have good food for the teenager too and a nice mountain view. If you're staying north of town you're just over an hour from the Old Rag Mountain hike, my favorite of Shenandoah.
Another bar food option that I remembered is Asado Wings & Tacos. And lunch: Moe's Original BBQ or Ace Biscuit and Barbecue. If you do take other suggestions to go to Montpelier, then check out Barbecue Exchange in Gordonsville on the way back.