Okay, I wrote this before I noticed that the criteria was public courses. So what? I'm not going to delete all of this, especially since so many on this board have little trouble gaining access to private clubs. It's still an interesting question -- which course in the state would you have to play to complete your resume.
After going down a mental checklist of my favorite courses in Minnesota, I have to echo Shivas and say there isn't a single course in the state that one would have to play to make his or her resume complete.
Interlachen? A nice relic of an earlier age, but I like it more for its Bobby Jones-related history than its actual design. An outstanding course, with a few odd holes.
Somerset? It's semi-template Raynor, and a blast to play, but I have to believe there are more pure examples of classic Seth Raynor in other states. Ditto for Minnesota Valley and Midland Hills.
Hazeltine? A good example of the beginning of the modern era of golf design, but also borrowing from the past. With all Reese Jones' tinkering, it's like Minikahda on steroids. I really like Hazeltine, but I can't say it's a course that every true design student must play.
Minikahda? I haven't played it in 30 years. They tell me Ron Prichard's 2001 restoration went well. Old-timers also say that when the original design was bisected by Minnetonka Boulevard, the course suffered irrevocable harm.
Woodhill? Played it once, along with about 500 other players that year. If so few people ever get on the course, how important can it be?
Minneapolis? Excellent tournament course, many terrific holes, but I don't know how many golfers are filled with love after playing it.
White Bear Yacht Club? Quirky, hilly, deceptive, strategic -- but not particularly representative of anything other than itself.
Northland? In a class by itself for views and, this year, firm-and-fast Ross in the north woods. But like White Bear, it doesn't represent a style of golf that can be repeated elsewhere.
Golden Valley? Love the deepened greenside bunkers and the holes with elevation changes, but there are a few too many ordinary holes for me.
Oak Ridge? Flat-out love it. Maybe it's the fact that it wasn't designed by a name-brand archie that keeps me from saying, this is the one.
Rochester CC? I've never played it, though people rave about this Tillinghast classic. From the pictures it looks wonderful, though maybe a bit over-treed.
The Quarry? A big, tough, option-filled golf course. Probably the best example of how good a new course can be in a rugged wooded setting. On the other hand, if I were going to pick one course, the Quarry's newness knocks it down a rung or two in a state filled with old classics.
And that's the problem -- I can't pick one old classic and say, "This is the course you have to play in Minnesota." Maybe my gopher brethren can do better than I have. I'd love to hear what they think, because I don't think there's a local consensus on the best or most significant course in Minnesota.