
The White River Badlands of South Dakota erode fast, and what comes out is one of the richest mammal fossil records on the continent: early horses, rhinos, oreodonts, and the false sabre-tooth Hoplophoneus. Fossils genuinely lie on the surface here. LOOK ONLY inside the park, and there is a public programme where you can report a find and have a palaeontologist come to it, which is a much better outcome than a pocket.
Oreodonts, nimravids, horses, rhinos · Eocene to Oligocene, ~34 mya
This ground is protected. Photograph it, record it, leave it where it lies. On US federal land the Paleontological Resources Preservation Act 2009 makes collecting vertebrate fossils an offence, and penalties are real.
Other places on the map within a couple of hours.