It shall be unlawful for any person, being upon the premises of any state park, site or facility of which the Kansas state historical society is trustee under the provisions of Kan. Stat. Ann. § 75-2701, or any amendments thereto, to damage, deface or destroy any building or part thereof located upon such premises, or any furnishings therein or thereon, or to damage, destroy or deface any lawns, trees, shrubbery, flowers, plants or equipment located upon such premises; or to park or drive any motor or other vehicle upon any part of such premises except upon the duly established drives, roads, streets or public parking facilities as indicated by signs, markers or notices established and posted by the Kansas state historical society or its duly authorized agents; or to exceed any posted speed limit on drives, roads or streets located on such premises; or to picnic or engage in sports or other recreational activities in any areas upon such premises except those designated for such purpose by posted notices or signs of the Kansas state historical society or its duly authorized agents.