I make a habit of going to Leesylvania State Park annually. This year we went for a Mother's Day jaunt along with taking Tavie for an afternoon walk.
The Park is essentially flat so the walking is easy. A high percentage of the visitors picknik so the aromas of cooking are fun. Kids seem to love to go in the water (cold or not and despite the warning signs). All in all, I can recommend this park as a "Happy Place". Additionally, the view of the Potomac River is excellent.
The charge is $4 per car, not bad at all.