The Quarry at Giants Ridge, maybe a little further away however
There is no maybe about it.
Meadowbrook actually butts up to Interlachen. It is one of the five Minneapolis city courses. It is a very good municipal known for its hills. Lots of blind shots, which some don't like.
Braemar, also in Edina, hosted a Tour event in the late 60s and a women's APL around 1980. It isn't going to knock your socks off but it is a solid course.
Stone Ridge, Chaska (2nd site for US Am when it was at Hazeltine), Rush Creek (APL won by Ryan Moore and also an LPGA site), the Wilds, Baker National, and Legends are your best bets for area daily fees. One post mentions the value (or lack thereof) at Legends...worth noting that rates have fallen this year and it is more like $75 instead of three figs.
Some others that are interesting are Willinger's, Stonebrook, and Fox Hollow.
Minneapolis has very good municipal courses. Hiawatha, Francis A. Gross (which I think held a PGA Championship), Columbia, and Wirth are the other four after Meadowbrook. You'd probably like Hiawatha.
Owatonna Country Club is a private course about an hour south, but they'll probably let you on if you contact them and say you are in town for the Open.
Have fun.