We spent five nights on the North Shore last August. We base camped at Tettegouche State Park -- beautiful park! -- and did day trips from there to see all the waterfalls. We spent time in all seven North Shore State Parks in five days. Here is a waterfall tour that is fun to do: http://www.onlyinyourstate.com/minnesota/waterfall-road-trip-mn/
All the waterfall hikes are fairly easy and don't take much time, but so worth it.
If you like bike riding at all, the Gitchi Gumi Trail is fantastic. We rode the section that goes from Beaver Bay to Gooseberry State Park.
Lots of good suggestions here so far. Have a great time!