The Guthrie theater, world class theater right next door in Minneapolis. If you live nearby I highly recommend getting season passes and enjoying all their plays.
Antiquarian books on Nicolette mall. Go ahead and pick up that ten thousand dollar map you've always wanted that belonged to George Washington.... Or something like that
Hennepin county library is a great place to visit, it's huge, and has a lot of resources available. Sometimes they have lectures in their modern auditoriums.
Interesting architectural apartments near lady Lourdes church. Notice the rose window near the top of the building, an obvious tribute to church architecture.
Franklin street bakery is an area favorite. They sell bread, pastries and other sweets. Be sure to take a glimpse at the giant factory in the back room.
Metro transit's lightrail system is fairly new to Minnesota, right now it runs from the mall of America to downtown MPLs. But soon it will also stretch through dinky town and the u of m.