You probably tried to get into Platte River C.G. at Sleeping Bear Dunes - just about impossible at the last minute. (We volunteered there) The park also has another campground - D.H. Day that doesn't accept reservations but you'd need to get there early morning.
Here are some parks just south of Sleeping Bear that you might try - gorgeous areas:
http://www.rvparkreviews.com/regions/michigan/frankfortWhile there, take the day ferry over to South Manitou Island from Leland and tour the lighthouse. (We gave the tours) :)
We're very partial to this whole area and it's a popular one for getting a campsite.
Interlocken State Park is nice if you can score a site. Take in one of the music concerts while there.