My humble recommendations -
You have to try a Juicy Lucy when in town:
Matt's Bar and 5-8 have both been mentioned, good Juicy Lucys can also be found at
Blue Door Pub
Sham-Rocks - On West 7th in St Paul
My favorite restaurant is a tie between:
Redstone
Axels
Other great places include:
Broder's Pasta Bar
Gasthof - featured on "Man Vs Food", very fun place
Fogo de Chao
If you are at Mall of America, the best places are:
Twin Cities Grill
Tucci-Benucch
Cossettas is best saved for non-game days, it gets nuts in there.
Micky's Diner is close to the venue, and is open late. Good "greasy spoon" type food, no booze.
Alery's is down the street from Micky's, the local cop bar, great fun especially after 9:00PM but no food worth mentioning.