Utica has a continental climate typical of upstate New York — cold winters with significant snowfall, warm summers, and pleasant springs and autumns. The best months to visit are May through October. Summers are warm without being oppressive, usually in the 24–28°C range.
There's no particularly compelling reason to time a visit to a specific season unless you're coming for the performing arts season at the Stanley Theater, which runs from autumn through spring. Utica is a city to visit for its cultural and culinary offer, not its weather.