The Emerald Necklace
Throughout its reservations in Northeast Ohio, the Cleveland Metroparks provides a series of paved all-purpose trails that serve as a recreation and transportation resource for cyclists. See their list of parks for details on each location.
You can pick your park and take a short, casual ride with your family, or string together several parks for an epic all-day ride.
While almost all of the parks have some amount of paved trails for bicycling, the longest routes that you can put together while staying on dedicated bike paths would include the Rocky River Reservation, Mill Stream Run Reservation, Big Creek Reservation, and the Brecksville Reservation. With a short hop on the Ohio & Erie Canal Towpath Trail, you could connect to the Ohio & Erie Canal Reservation and the Washington Reservation, or using the Carriage Trail Connector, you could also connect to the Bedford Reservation and the South Chagrin Reservation, with a brief on-road connection from there to the North Chagrin Reservation.