While weather is unpredictable here in May and June, I prefer coming here then. It's quieter and less crowded. If you like solitude and the spartan amenities car camping can afford, I highly recommend Hurricane River. But it can't be emphasized enough: the weather could be pleasant, but also very likely to be very, very, very lousy. Prepare for freezing rain and winds, and yes, snow in May is not unheard of (one May, I once woke up to a blanket of snow on my site at Sleeping Bear Dunes, which is farther south, so I imagine May snow in the U.P. is not unusual).