The only way in, and the only way out at least by car, is U.S. Highway 61, which parallels Lake Superior. There are other roads that leave town, but they just head into the woods and eventually stop. Highway 61 is the only paved through road in Cook County, so enjoy it. As a historical note, Highway 61 didn't open until the 1920s; before that, most travel to much of anywhere was by scheduled steamer on Lake Superior. This meant, of course, that between sometime in November and about April, there was no service due to ice. During that time, you had your option of horses or dogsled, but this was confounded by the fact that there was really no continuous road where highway 61 is now.
There is an airport (http://www.airnav.com/air...) a few miles out of town, up on the ridges overlooking the lake, but no scheduled service.
And of course, you can boat in via Lake Superior. There is a municipal marina (http://www.grandmaraisrvp...) to dock at and get fuel. The harbor generally has a few fair-sized sailboats or powerboats in it, often having sailed across the lake from the Apostle Islands. Boating on Lake Superior isn't necessarily dangerous but isn't for novices, either. The State of Minnesota has created about 15 "safe harbors" up and down the North Shore, because there are virtually no natural harbors along this 130-mile 209 km stretch. There's a reason they're called "safe harbors;" think about it before you just up-hook and set out.