Thanks all and for your advice.
We did go to Block Island and it is a wonderful place. It is really beautiful and a great natural area. We pulled up to a mooring in Great Salt Pond, the "new harbor" at about 6:00 in the morning. We didn't call anybody in advance and we knew just to look for the "Granny Smith green Apple" colored balls. There were plenty available all of time we were there. The first one we tried and the little floating part that holds the line was tangled around the mooring chain and we couldn't untangle it so we went to the next one - #67 - and it was a breeze. We just reached for the floating buoy with a boat hook and pulled it in. The line that is connected to the mooring has the right amount of line to bring straight to the anchor chock. The harbor master came by soon to collect the rent. They were $30 a night.
I will say that one concern I had is that we have a long bowsprit and thus bobstays supporting the stays at the end of the bowsprit. Since our anchor chocks are way back I sort of felt like I needed a bridle of some sort to even the pull on the two sides of the boat. We were just attached to the mooring ball on one side and it was about 3 feet back from the jib. When the wind blew a certain way the mooring line would put pressure on the bobstay (see the photo).
I could have made a bridle of some sort, or tied another line to the ball, but it never got stormy while we were there so I didn't worry about it. I wasn't sure how that one line was supposed to work with a boat like ours, and when we picked up a mooring at City Island in New York it had two lines coming from the mooring. This was much better since it balanced the boat to the center.
There is a very convenient shuttle taxi from the moorings to a landing. It's a great way to go. We would use the dinghy to save money sometimes, but when your "all primped up" and ready for a night on the town it is nice to just call the shuttle guys and get onto a sturdy platform. I think it was $3 per person and we had 5 people and we would always tip, so after a while the dinghy had its appeal.
Great Salt Pond was formerly a fresh water lake; a big one. It was turned into a salt water pond at some point and thus the name "new harbor." Many people said you should definitely stay at the new Harbor. The old harbor is just a jetty with room for a few boats on the eastern side of the island. But if you were able to get a mooring there it would be more central to the town. From the Great Salt Pond it is a couple of miles walking, or bicycling, or an expensive taxi. The new harbor is right there.
I highly recommend Block Island as a cruising destination. It is a very beautiful Island and is 75% owned by the nature conservancy. There are great restaurants all around and it is a fun island atmosphere. You can walk, rent bikes and boats, take taxis to get around, shop etc and the views are really impressive.
One of our brave crew members went to the top of the mast to take this picture of the Great Salt Pond at Block Island. Its a beautiful place!