If you're going that far up then I recommend taking the Brockway Mountain Drive just West of Copper harbor. Very scenic.
Click here: Brockway Mountain Drive - Upper Peninsula Wiki
Ft. Wilkins is a must- give yourself a few hours there to take in the history.
Copper Harbor is a bust actually. There's no pretty beach to enjoy. If you would like to see a beautiful sandy beach with some rock overhangs (where you could eat a lunch & look down on the town) then Eagle Harbor is the place to visit. Most people miss it on there way to Copper Harbor.
Click Here: Eagle Harbor and Eagle River Michigan in the Upper Peninsula on Lake Superior
Oh, and don't try to take firewood across the Mackinaw Bridge sometimes they check us campers out....