Just a suggestion, depending upon when in June you plan to travel, but you might consider starting out your trip in the lower Great Lakes. I've lived in northern Michigan and the Upper Peninsula and the early part of June can be a bit chilly. Of course there are never any guarantees regarding the weather, but you'll likely find better weather conditions further south in early June.
Additionally, the Great Lakes act as a climate buffer for areas along the coasts. The water is cooler in the late spring/early summer and that keeps those shoreline areas cooler as a result. This is why the west shoreline of Michigan has so many fruit/vegetable farms. The cooler weather helps to prevent plants from developing too quickly in the spring, thus helping to limit the amount of frost damage from a May or June frost.
June is strawberry time with cherries and blueberries coming along in either late June or early July. You can also find fresh asparagus in early June from SW Michigan, but you'll more likely find some just a bit further north south of Ludington and a bit north too.
I'd suggest starting along Lake Michigan in the south and work your way north from there. In the U.P. the southern portion will be warmer compared the Lake Superior. You may want to jump on some state park reservations. Michigan is switching to a new reservation system starting November 1, 2013. The system has usually allowed reserving a campsite 6 months out. Suggestion for consideration would be Van Buren SP near South Haven or Ludington State Park or possibly Charles Mears SP in Pentwater. You're more likely able to get into one of these in early June rather than late June. They are popular.
Good Luck with your trip planning.
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