The twin cities are famous for the juicy lucy's. There are a lot of places to buy a juicy lucy and everyone has their loyalties. In it's purest form a juicy lucy is a hamburger with cheese on the inside of the hamburger patty. Pretty simple yet not very common elsewhere. A lot of places will make their juicy lucy's different by adding different toppings and other items.
I would recommend a handful of restaurants:
- Blue Door - get to the place early because the restaurant is small
- The Nook - there is an old school bowling alley in the basement and their happy hour is quite nice
- Matt's Bar or 5-8 club - these were the originals I think.
There's more but this is a good start.