Depends on just how remote you want to be. Broadband is available in the more populated towns. When I was in Houghton, the only major service interruption I remember was from a backhoe operator digging where he shouldn't.
Most of the towns in the area have decent internet, although I remember having a lot of outages, at least a few every winter during bad storms. I'm not aware of any gigabit connections but the speeds are enough to stream movies, play games, and fiddle around online. If you go off into some of the more remote areas, like 10-30 minutes outside of a town, you're largely stuck with satellite internet.