Our local library had several great travel book about Ohio. My favorite is Kids Love Ohio, which has tons of unique travel ideas for the state divided in different geographical regions. There are so many great things we have done thanks to these books such as a trip to the Amish country, local museums, fossil sites, festivals etc.
Some of the places are free, but you could make "tickets" or certificates to be used over the summer. We usually designate summer Wednesdays for day trips that we have picked out ahead of time. It makes our summer fun and we get to explore our state.