John;
Although Cape Cod and the Islands have over 75 courses, if one of your ancestors didn't make the trip over on the Mayflower, access to the upper tier can be quite problematic. The terrain is very sandy and the ever present wind causes the local trees to be stunted, oaks and pines not more than 12 feet tall. You'll find that most all of the old private clubs have a linksy nature with firm turf, and greensites which accept the runup shot you'll need to stay under the wind. If you can wangle an invite to Kittansett, Oyster Harbors, Wianno, Hyannisport or Eastward Ho!, drop everything and take the opportunity, you won't be dissappointed. Although there are a lot of newer public courses such as Cranberry Valley, the Captains and the like they don't really take advantage of the sandy terrain to provide a true links experience; call it parkland golf on sand! New Seabury is a very nice modern course (1960's) with a seaside and wooded nines but does not allow outside play from May to October. My recomendation for the best 18 hole public access course is Plymouth CC, just over the Cape Cod Canal. It's a Ross from the 1920's and the public is welcome during the week at a reasonable price. The Plymouth area is Mass. newest golfing hot spot with new courses by Rees, Jack Jr., Brian Silva and I believe a C&C now under construction.
For just plain fun I would recommend playing the three 9 hole courses though. Highland Links is quirky and fun, in nearby Wellfleet is the Chequesett Yatch Club, a 9 holer biult in 1926. Last but not least is "Little Marion" George Thomas's first foray into golf design. Also over the canal in nearby Marion, it is located on Point Rd just before reaching Mass.'s second best course Kittansett. Also built in the 1920's it makes good use of the rocks that littered the site before construction. Several greens are surrounded by stone walls, and there are huge berms created by piling the rocks and covering them with turf; we used to call it the "Indian Burial Grounds". Farm Neck is surely the best golf on the Vineyard, but since being popularized by Bill Clinton, is very busy. Have a great time in the Bay State.