I would also recommend Bethpage, there are 5 courses I believe, all named by color. Black is obviously the one to play and the hardest to get on. I've played that once, and it took us two tries to get on. If you are going to try to play that course and you are NOT a residence of New York, there are a few hoops you will have to jump through. If you are military as well, they do a very generous military discount.
The rest of the courses vary in difficulty and are not as hard to get a tee time for. I would put this on a bucket list if it's not already.