Near The Sleeping Bear Dunes National Lakeshore . . .
I'd recommend September. Weather is moderating and the summer tourists are gone. Can't remember the last time I've gotten a mosquito bite around here. There are nice routes and some trails in Benzie, Leelanau, and Grand Traverse Counties.
New for 2019 is going to be an extension of the paved portion of the Sleeping Bear Heritage Trail through our National Lakeshore. It's always a nice ride N into Glen Arbor for lunch. One 13% grade hill along the way and you can stop for a dune climb or at the old logging and canning village of Glen Haven for a great view of the Manitou Passage and islands. The trail N of Glen Arbor is problematic as loose gravel makes riding my trike there excruciating and I take to the roads.
Another favorite trail is the Leelanau Trail to Sutton's Bay. One may start at several points along the way. Two wineries, Shady Lane and Black Star Farms, on roads close to the trail are worth the stop. The reds up here are not great, but the whites are exceptional.
Backroads are generally safe for cyclists and there are many good routes, especially on the Mission Peninsula above Traverse City.