I'd go for Syracuse too. Smaller airport, easier to drive in and out of and much closer to Watertown.
Alex Bay is, distance-wise, about as far from Fort Drum as where I live, but it's a more difficult drive since you either have to take 81 to 12, or take 26, which is a little two-lane road with no shoulder for most of the way. Just FYI.By the way I found a landlord in Alexandria Bay. He said to email more info about us, how we live, pictures of the dogs (he has a dog himself) and I sent him some of the videos from the dogs. Pics of how we live etc.