Central Ayuthaya is on an island at the confluence of three rivers. You can hire a longtail boat to cruise right around the island, which takes about an hour if you do not stop to look at temples and much longer if you do stop. The experience is fun and the cost modest. Boats for hire can be found on the riverbank near the intersection of Thanon Pamaphrao and Thanon U Thong in the north-eastern corner of the island.
During my boat ride we saw at least two enormous lizards almost 2 metres long swimming in the river. They were moving much too fast to be photographed.