About one and one half hours south east of columbus is hocking hills state park and the related caves in the area. you need to head out of columbus on rt 33 and start looking for signs to old mans cave, Ash Cave, Rock House and Cantwell Cliffs etc. This time of year will be crowded but during the week should be slower, if not wait until october.
pull them up on the web, there are tons of cabins in the woods with hot tubs and fireplaces, horseback riding in the mtns, mom and pop restaurants and camping.
also you are not far from the best whitewater rafting in this part of the usa. come sept and october the white water in west virginia at the gauley is class IV and V all the way. http://www.rivermen.com/
you are only 5 hours or so from that but book early as there are only 10 days or so when they release water from the dams.
columbus has a great market not far from the downtown donvention center and of course the little shops around that area are great. very individual.
you have the newport for intimate music across from the university on high, and polaris amphitheater for outside concerts.
you have the big darby http://www.bigdarby.org/
in columbus, one of the top rivers in not only the state but eastern us. they have a canoe trip this weekend. it is on the natures conservancy spotlight.
lots of great restaurants. theaters too. lion king was there recently. ohio state fari starts in august. look up columbus city on web for this all...........