A small but worthwhile natural history museum on the Miami University campus, the Limper Geology Museum contains rocks, minerals, fossils, and geological specimens from around the world. It is particularly strong on Ohio geology, which is more interesting than it sounds — the state sits atop significant Ordovician and Silurian rock sequences, and the fossil record from the region's shallow ancient seas is rich.
The museum is free and housed in Shideler Hall. It's the kind of place that rewards curiosity: a few well-presented specimens can change how you look at the flat ground under your feet. Budget an hour.