You can take time to visit The trail to Copper Harbor during your travels to Hancock. Amble around the area's lakeside, or seek out its hiking trails.
Though Portage Health might be what brings you to town, perhaps you'll have a chance to explore more of Hancock while you are here.
You can find out about the history of Hancock with a trip to Quincy Mine. You can seek out the ski slopes and hiking trails in this walkable area.