This park is wonderful for hiking. The trails are manageable even for families. Many areas for picnicking. There is a road to drive on so that you're not just stuck in the middle of a forest with no way out. There is a sort of dam that is great to look at...it has a waterfall that fascinates kids. Great for exercise and as a vacation paired with camping. The view from the top is wonderful as well!
Paris Mountain is a state park in Greenville with lots of options for hiking and biking. What I like about this park is the closeness to Greenville as well as the great parking near almost every trail. So, if you're hiking with little ones, it's easy to get right on the trail. The park is beautifully maintained and near the entrance there is a short one mile hike for the small ones around a lake filled with wildlife for kids to enjoy.