I have family in Old Saybrook and have played quite a bit in that area.
Fenwick is great. Small, pushup greens. Unirrigated with great views of the sound (and Katharine Hepburn's mansion to the right of the second hole). And a wonderful cape hole over south cove to boot. But its only 9 holes and the conditioning is what you would expect for the price ($20 in November for 9).
I also would second Shennecossett. Nice old ross with some really good greens, although some holes are newer due to a land swap with Pfizer. It is also public, but I thought in very good shape for the price.
Fox Hopyard in East Haddam is a Rulewich design and semi-private. It's in great shape and but not as interesting architecturally as Shenny. I would also second Shelter Harbor and say CC of Fairfield is fantastic if you want to drive an hour. Both are very private. I have not been to the other private clubs in the area, but Madison CC looks great from the street.
Restaurants: Grano Arso in Chester is off the charts and very worth the drive. In Saybrook, Liv's is great as is Cafe Routier in neighboring Westbrook. Saybrook Point Inn is pretty but the food is over-rated. And downtown Madison is delightful -- don't miss the RJ Julia bookstore.