You are doing yourself a disservice if you don't play this course. Open to the public after Columbus Day, they keep it in great condition even after most of the membership has fled the island for the summer. It's a gorgeous old-school links layout. Try not to get distracted by the scenery on the front 9.
We lucked out on a late October trip and had a cloudless, windless, high 60s day to play 36. One of the best - if not the best - days of golf I've had in my life. Year before I played in 30 mph wind and despite my worst score of the year couldn't wait to get back. Just play here. Blows away most of the upper echelon public courses on the mainland. As a Nantucket native I'm proud and happy to know my island holds a true gem like this.