I did the Stock Exchange tour with Magic111 last month during the NYC get together. We went by around 10 in the morning, and the next available tour was around 1:30. They hand out free tickets, which we needed when we came back later, and there is a limited number per tour. Might be better to arrive when they first open up.

You can get in by subway from JFK. You have to take the free bus to the Howard Beach station, which adjoins one of the outer parking lots. I've done that before without any problems during day time hours.