You're forgetting Rome, Attica, Utica, Corinth, Camilius, Seneca, and a lot of others. The majority of towns you're referring to fall into what's called the Military Tract, it was a section of the state set aside to be used as payment for New York soldiers from the Revolutionary War. As part of getting this organized, they first created town borders, and then named them.

Some attribute the names to Robert Harpur, and others to Simeon DeWitt.

Source: Classical Place Names in New York State by William Farrell