There are plenty of day hikes in Shenandoah not far from Luray or Shenandoah Woods. It costs $30 to enter the park in a vehicle or $15 to enter on a bike. National park passes also accepted. Passes are good for 7 days. The closest entrances are Thornton Gap and Swift Run Gap. There are numerous hikes appropriate for all levels in this part of Shenandoah. Check out maps for the North District if entering through Thornton Gap and the Central District if entering through Swift Run to see what's nearby.
The George Washington and Jefferson National Forest is also easily accessible from Stanley or Luray and is free to visit! The Kennedy Peak trail offers great vistas and is a great run or hike for someone with strong trail legs. Several other nearby trailheads include Scothorn Gap/Duncan Knob Trail, Massanutten Storybook Trail, and Lions Tail Trail.
Luray caverns is the largest cavern on the East Coast, with cave formations that sing and cavernous rooms as large as 10 stories high.