Scroll down in this "RockHounding Locations" to the Nethers Farm thread for Flint Ridge information.  Not sure if it's still open; I have yet to check it out myself when travels take me to Ohio.  Flint Ridge is east of Columbus, so it will be about a 90-minute drive from Dayton.  Also, see
http://www.newark.osu.edu/facultystaff/personal/jstjohn/Documents/Rocks-and-Fossils-in-the-Field/Vanport-Flint.htm (This Ohio State geology professor has a very interesting web site with lots of photos of interesting geology worldwide.)

Closer to Dayton you can find plenty of fossils at Caesar Creek Lake State Park.  The park may still have an area designated for collecting like it did in the '90s.  You can also strike out on your own in the various creeks.

Also worth a trip is Serpent Mound in southern Ohio a few hours from Dayton.  The ancient mound itself is impressive,  and the adjacent area is thought to be an eroded impact crater.  The impact was likely responsbile for the high number of minerals found in Adam County, although in small quantities per an old state geologist's book I have somewhere.  We took the kids to Serpent Mound a few times when they were young but never hunted for rocks and minerals.  I wonder what creek crawling in the area would turn up.