My personal favorite is Cranberry Valley in Harwich, followed by the Captains in Brewster, and Hyannis Golf Club off of exit 6 on the mid cape highway.... These are all public, Cranberry Valley is a terrific course, and the Captains has 36 there, I really loved the original 18, the new 18 is intermixed with the old to create the 2 courses. I liked the new holes, but I really liked the old course the way it was, just my opinion, I played it for 15 years the old way.........
If you have connections and can get on, cant go wrong with Hyannisport or Eastward Ho! both private...There is also a decent public course in West Yarmouth called Bayberry Hills or something like that. It was a bear when it first opened, havent played it since 1999, but it was pretty nice, hard though.
The is a 9 hole course in Chatham, Chatham seaside links, that I think is public....looks pretty wild, but I havent played it.
Hope this helps.....I would tell you to go to a Cape League game, but they dont start until the middle of June.