Off the top of my head: beaches are the only thing, in the USA, I can think of that are always public and you can always cross private land to reach.
Upstate New York's Adirondack State Park is over six million acres of forest, mountains, lakes, and streams -- the largest state park in the continental U.S., almost as large as the entire state of Massachussetts. Half of the land in it, is actually privately-owned. Years ago, I hiked and camped there a lot, and frequently hiked along a state trail, only to find myself tramping across someone's backyard. And that is perfectly acceptable there. Very little land in the Adirondacks are truly off-limits to hikers, and it is very clearly marked. If you buy property there, you just know that hikers may be on your land. It's part of the deal. Your house is still private, but your land is fairly open access.