Detroit, Michigan. You can get a house for $500 on a mountain of despair next to a lake of misery.
Single Family Home - DETROIT, MI, 48213 - Realtor.com
Baraga, Michigan.
Single Family Home - 14614 Payne Rd, Baraga, MI, 49908 - Realtor.com. Little above your price range, but close to the water. Baraga is at the top of a mountain, and close to some decent skiing.
Calumet, Michigan. What a steal at only $40k!
Single Family Home - 58302 Calumet Waterworks Rd, Calumet, MI, 49913 - Realtor.com. Fixer-upper.
Houghton, Michigan is a nice area. Lake Superior is an easy drive in multiple directions. Housing is very cheap there. Tech university in town (Michigan Tech). Small. Lots of big hills and small mountains. The downside (or upside) is that the homes have docks off of their front doors so people can get out in the winter. Many a Tech student has a story of jumping out of the second story window into the snow. Winter lasts from mid-October to late April. However, the Keweenaw Peninsula is some of the most beautiful country in the US (imho).