I work at a hotel and regularly suggest checking out Trammel Fossil Park. This park is not off the beaten path, but it is "hidden" at the end of a business park. There are port-a-potties, a place to wash your hands, picnic tables, educational plaques (these tell you about the ecosystems and which fossils were abundant then), and the main event--fossils galore.
You do not need to bring any special equipment, except a bag for carrying your finds home. This is because the fossils are so abundant that you do not even need to dig for them. Your finds can include everything from coral to trilobites (Ohio's official fossil)!
There is a woods at the top of the hill with paths crossing through it. The paths are neither paved nor marked, so use discretion if you do not have a great sense of direction or not a lot of time to spare. I enjoy fossil hunting in the creekbeds you will find along these paths.
Be sure to wear good shoes, because there are no paths leading to the top of the hill or along the hill where the bulk of the fossil hunting occurs (you will be doing a little climbing). Trammel Fossil Park is not "handicap friendly," so please keep that in mind, as well.
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