If I was driving from southern Michigan, I'd probably head north and ride the back roads. ridewithgps.com can search for routes. For instance, these routes within 50 miles of Traverse City
I like stapfam
's idea of morning rides from a base location.
For someone closer to southwest Ohio, there's a lot of interesting riding here.
I live near enough to the Little Miami Trail to ride it regularly. For peace and quiet, the section north of Loveland OH has far fewer walkers, skaters, kids on bikes, and road crossings. It follows the old train track route along a wooded valley. Loveland to Spring Valley map
There's water stops every 7-10 miles.
I'd also suggest doing the 8:00AM Saturday Breakfast Ride from the Cincinnati Cycle Club. This route is marked with spraypaint, and can have over 50 riders in nice weather. So it breaks up into smaller speed groups as riders find compatible riders in the first few miles. It has a restaurant stop at the halfway point. Outbound map Return map
I had driven in the area, and all I had seen was flat cornfields. Boring. But the Breakfast Ride mostly follows obscure back roads with almost no traffic, and it's pretty scenic. There's stream valleys, woods, and historic brick farmhouses.
For any of our weekend rides out into the country, even just 20 miles from the city, we rarely see much traffic. Of course, we stay off the major highway routes.
I'm sure any place you visit will have some good bike routes. The locals have been riding and refining their choice of the best bike roads for years. Try to find the ride schedule for a local club.
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For me, the best riding by far is 6-7 hours south on the Blue Ridge Parkway. It's perfect for bikes.