Part of a larger county park system, Big Creek Great park has a little bit of everything. Most of the trails are small, well-marked, accessible, and easily walkable for families.
As far as camping, there are two rent sites (A and B), two lean-to sites (C and D), plus a tree house :) Really cool structures that are available to rent through the website.
Quick tip: Bring some fishing rods! There are a few ponds on the property, complete with fishing docs, that are stocked with bluegill and small man fish. Have at it!￼