The tasting room with a fire going. The bookstore that doesn't mind if you stay two hours. The museum nobody on TripAdvisor mentions. Rain on a lake is one of the better problems to have.
The reason Oneida's walleye fishery holds up as well as it does — this hatchery raises and stocks the fish that help the lake rank third in New York for angling. The visitor center has a viewing area where you can watch fish get unloaded from the boats, plus tanks holding species you'd otherwise only see on the end of a line. Free, open all season, an actual reason to detour to Constantia.
Reconstructed 18th-century blockhouse on the site of a 1759 British fort built to guard the Albany-to-Oswego supply route — an eight-pointed star fort with room for 130 soldiers in its original form, dismantled by 1767 under treaty terms. The museum inside covers 10,000 years of local history, further back than most lake-town museums bother to go. A slow Tuesday-afternoon stop, not a full day.