I have been to Mac twice.  I would be surprised if you can get a place to stay on the island or even nearby.  Sorry to say that.  Oh, the Grand Hotel on the island might have rooms.  $1,000/night per room.  Our accountant went a few years ago and told us about his stay there.  

We are going to WI July 23-29.  Oshkosh for 2 days.  We like saying in Waupaca.  B & B at the chain of lakes.  We take the old big wheel paddle boat out for the 1 hour tour.  You get to see the youth camp on an island and all the other lake side homes.  Fun for a small town Ne. guy.