I was born and raised in Cleveland. The Cleveland Metroparks encircle the city with over 80 mile of parks and forests. Lake Erie offers many interesting opportunities for various water activities. The Rock and Roll Hall of Fame is in Cleveland, near a wonderful lake front park. Early to mid October can present great fall colors throughout the parks.
If you travel down rt 83 to Millersburg (about 60 miles), you'll be in the heart of Amish country. Horse and buggies, rolling hills, rural farms, very scenic all year round.
If you have a free weekend, make a trip north to Canada's southern most Park, Pt. Pelee National Park. Noted birder and author, Roger Tory Peterson, called the fall hawk migration at Pt Pelee, one of the 10 greatest birding experiences in the world. Early to mid October is best for the migration. It is about a 3 to 4 hour drive, lodging is available in Leamington.
Post back what interests you and I'll try to be a bit more specific if you like.