Excellent indoor conservatory that has 5 different gardens, including everything from bonsai, ferns, flowers, and tropicals. It's a great place to go anytime of the year (it's especially welcoming in winter), and admission is only $1.
Visit the Sculpture Garden, drive down Summit Avenue, see a St. Paul Saints minor league baseball game in the summer (if you can get tickets!), visit the Mall of America if you must, walk around Uptown and Lake Calhoun.
This museum in downtown St. Paul is huge and has displays of everything from the Human body and genetics to Dinosaurs.
When in Saint-Paul, one should see Summit Avenue. Summit has many early 20th century houses and is a lovely street to walk in.
Saint Paul is a nice town to wander around in. If you're in the Twin Cities, might as well see them both.