Copper Harbor is just short of the northeastern tip of the Keweenaw Peninsula and the end of US-41 (from Miami). Take either US-41 or M-26 north from Houghton-Hancock; the two routes share roadway part of the way, with the state road taking a couple of detours. When they split at the crossroads of Phoenix (about 8 miles north of Ahmeek), you have your choice of routes: M-26 meanders along the Superior shoreline, US-41 "tunnels" through a lovely canopy of trees, and Brockway Mountain Drive (accessible at Eagle Harbor from M-26) follows a ridgeline and offers some great views (but is not plowed in winter and has some very steep grades).
The city is on a harbor of course, but the only commercial service is to and from Isle Royale National Park.
The city is clustered around the harbor, with most places within easy walking distance. Bicycles or cars will get you further afield.
There's a series of trails in the hills outside of town, suitable for hiking and some for all-terrain biking.
Harbor Haus American German Restaurant, Keweenaw Mountain Lodge
Copper Harbor is one of the main gateways to Isle Royale National Park over the horizon in Lake Superior. The Keweenaw Peninsula itself is host to a plethora of hiking, biking, fishing, or skiing opportunities.