In Duluth, make sure to stop at Canal Park and watch a big ship come into port. Others have mentioned other places ... Gooseberry, Split Rock ... lots of beautiful state parks nearby.
In Minneapolis, I tell everyone to visit the Mill City Museum ... very interesting, very worth it. Then head to the Mill Ruins park and walk across the Stone Arch Bridge and follow the trails around the other side. And then walk down to Nicollet Island.
The Walker Art Center and the Sculpture Garden.
Minnehaha Falls.
Those are some of my 'go to' places in Minneapolis.