Lots of possibilities.
The newer "Tow-path" path might be one of them. It does mean first riding South through the industrial river Flats, but on a Saturday auto traffic should be light. The pave part of the path starts at Harvard Rd. then South to Rockside Rd. it continues South as a crushed rock path for a long long way. Or you could ride in the Metro Parks Rocky River valley just West of the Spin shop. Or the residential areas near the lake shore West & East of the city.