Lots of snowbirds flock back to the Keweenaw Peninsula every summer.
If you're looking for something "in town" you won't have any problem finding something under 80k, but that would be on 50x100' city lot.
Waterfront is available, but supply/demand forces these prices up.
If you don't mind being a little isolated, you can try Keweenaw County. Lots of fresh air, very few neighbors.
The summer pace up here is decidedly slow and low-key (no MTU students). A bonfire and some cherry-wine is a Saturday night.
You've probably checked these websites, but here's a taste of life in 'da Keweenaw'
Keweenaw Convention & Visitors Bureau
Welcome to Pasty Central
The Daily Mining Gazette
Welcome to the Official Web Site of Copper Harbor
and here's some realty websites to get you started:
Moderator cut: linking to real estate sites is not allowed
Grand Marais is nice, too.
Maybe rent for half of a summer at each place, then decide wear to set your stakes?