There is a fish hatchery in Powder Mills Park. It was bought by a private individual and later turned into a not-for-profit organization.
There is also the Caledonia Fish Hatchery, operated by the New York State Department of Environmental Conservation (NY DEC) in the nearby village of Caledonia. It is open daily for self-guided tours, 08:00-16:00. The drive from Rochester out to Caledonia is quite scenic (about 23 miles or 35 mins).
Look at the pretty fish. Throw in some fish food (available from dispencers for a quarter) and watch them go crazy.
Caledonia Fish Hatchery
16 North Street; Caledonia, NY 14423. Phone: 585-538-6300
From a pamphlet available at the hatchery:
Caledonia Fish Hatchery is rich with history. The first fish hatchery in the entire western hemisphere, Caledonia was founded in 1864 by the father of fish culture, Seth Green. Many of the facility's buildings, including the main hatchery buildings are the original structures that date back to the 1870's.
In 1870, Caledonia was acquired by New York State. Today, the hatchery primarily raises brown trout, including nearly all of New York State's two-year-old brown trout. The larger browns average over one pound and 14 inches in length, and are stocked into many waters across the state—from Long Island and the Catskills to the Adirondacks, and from Central New York and the Southern Tier to western New York. In addition, Caledonia also raises up to 500,000 chinook salmon each year.