Name a town located on the southern shore of Lake Ontario in New York.

Rochester is indeed a town situated on the southern shore of Lake Ontario in New York. It is one of the largest cities in New York State, located on the river's banks a few miles from the lake itself. The city has a rich history tied to the development of the canal system and industry in the region, making it a key area for both commerce and transportation.

The other towns listed do have connections to Lake Ontario, but only Rochester is directly on the southern shore. Syracuse, for example, is located further inland and is not directly adjacent to the lake, while both Buffalo and Watertown are situated at different points relative to Lake Ontario; Buffalo is positioned at the extremely western part of the lake, whereas Watertown is located much further to the northeast, in a different geographical context. Thus, Rochester is the correct choice as it represents the southern shoreline's offerings and significance.