Quincy Mine (right in top of the hill in Hancock) is offering daily tours through the 17th. Personally, my favorite place to go for mining history is the Calumet Visitor Center - three floors of modern, well put together exhibits for free!
The Hungarian Falls Complex is what I consider the nicest set of falls north of the bridge, and is a relatively short (1-2 miles) hike to see all of them. Eagle River Falls is probably the easiest, most worthwhile falls to visit that doesn't require any hiking. Jacobs Falls and Haven Falls are two falls that are also located right next to the road. (However, if you are interested in hiking, let me know and I'll throw out some more spots.)
Despite being past peak, Brockway Mountain Drive and Cliff Drive are great roads regardless of the time of year.