Arrowhead Pointe, which is a state park course inside the Richard B. Russell State Park near Elberton, GA would count not only as one of the coolest munis, but also among the greatest Hidden Gems in the world. I believe Arrowhead Pointe is now #5 or #6 on the Golfweek Best Munis list, and it is every bit that good. On top of that, it costs under $50 to play, even on a weekend, and there is NEVER anybody on the golf course. I cannot recommend it highly enough.
As far as "cool", though, it's hard to beat the Dr. Charles L. Sifford Golf Course, in Charlotte, NC. Originally called Bonnie Brae, it was the first public course in Charlotte/Mecklenburg; 18 holes until I-77 ate 9 holes. More significantly, the charter under which the land was donated specified that it would always be a golf course, and that the golf course would be "White Only". Sifford, who grew up in Charlotte was, of course, unable to play there until after a landmark civil rights case in the '50's. The remaining 9 holes were reworked (by either Tom Jackson or Clyde Johnston; forgive me for not remembering which) and are the home of the First Tee of Charlotte. On each tee box is a monument with a plaque detailing both the history of the course and Sifford's remarkable career. THAT is cool...