Perhaps it is a coincidence, but I rarely see submarines in the summer months. During September and October however, I see them quite frequently. They move along at a good speed and have a habit of sneaking up on you. Despite being surfaced, they seem to blend in with the horizon, until you eventually realize that a portion of the horizon is moving towards you.
My first encounter with a submarine occured about 25 years ago between Montauk and Block Island. It was also the scariest. With no other boats around and a relatively calm sea, a submarine surfaced on our starboard side. I don't recall how close it actually was, but it's sheer size made it appear to be right alongside us. I still remember the 5 seconds or so, where I did not know exactly what was happening. It was as if the ocean just opened up.
I have yet to visit the USS Nautilus Museum in Groton, but it is on my rainy day list. According to its website, it has the largest collection of submarine artifacts in the country. Visitors can also tour the USS Nautilus, which was the first nuclear powered submarine. Admission is free.