I used to live in Branford not too far from the Elks club, so I thought I would chime in as well. I live in NC now, so unfortunately I won't be able to attend.
One that was not mentioned in the other posts was Faulkner's Island (best pronounced with a NY accent) in Guilford, which is the next town north of Branford on I-95.
You can only see it from the harbour, but Guilford is a very quaint New England town. To get there you just drive to the town square and head to the marina area. There is a town parking lot that I think is actually considered a small park.

As for Stonington, I think that is the best of the lot in the State. New London and New London ledge are on the way to Mystic and you cannot get too close to New London as the owner has posted a sign that trys to prohibit you from even taking pictures. You can also see New London ledge from that spot as well.

As for Bridgeport, well....
I went to the University of Bridgeport years ago and Seaside Park was nice during P.T. Barnum's heyday, but it is not a good part of town to send anyone. At times, the crime in Bridgeport is worse than crime in NYC. That part of town is dirty, grimy, full of crime and that part of Long Island Sound smells. I would suggest skipping it unless you did not have a problem getting lost on the wrong side of the tracks. From what I understand the campus has also gone downhill too. If I had to chose between seeing lighthouses in New Haven and Bridgeport, I would prefer New Haven.

Other than that, have a lovely time.
If you are hunting for pieces, one of the dealers is Hilltop Orchards in Branford (though technically I think they are in North Branford). They also sell pumpkins, apples and wonderful cider. They should be within 15 minutes of the event.