A couple places I would suggest (I'm a MN local): For a Juicy Lucy, I would suggest the 5-8 Club (South Cedar - next to airport). You can also get a taste of the Minnesota Lakes by walking from the 5-8 up to Lake Nokomis (3 blocks). It's not as peaceful as other lakes (airport noise), but a nice 2-mile walk around the lake.
If you really want to get a "lakes experience", I would suggest the chain of lakes south of D.T Minneapolis. Lake Calhoun always has the most going on and the people watching is outstanding - it's a 3-mile walk around.
For breakfast, I would suggest the New Louisiana Cafe in St. Paul (Selby & Dale). If you're in to hearty breakfasts, that's the place.
One place that hasn't been mentioned on Gameday is Blarney's Pub about 1/2 mile from the stadium. It's a great Irish college pub that is great on days of game. Nice selection of Whiskey/Bourbon too. The appetizers there will be enough to fill you up. Good selection of beer.
The other places that have been mentioned are all good, but these are some of the local favorites that are out of the way.
A couple more places: if you like eclectic/crazy I'd check out Betty Dangers in NE Minneapolis. Psycho Suzi's has a great Bloody Mary Bar (also in NE Mpls).
Enjoy your stay.