The Italian city-state ruled by the Sforza family during the Renaissance was Milan.
More precisely, the Sforza ruled the Duchy of Milan, a powerful state in northern Italy. Francesco Sforza, a successful condottiero, became Duke of Milan in 1450 after the extinction of the Visconti dynasty and the brief Golden Ambrosian Republic. His marriage to Bianca Maria Visconti strengthened his claim to the duchy.
Sforza rule included several notable Renaissance rulers, including Galeazzo Maria Sforza, Ludovico Sforza—known as Ludovico il Moro—and Francesco II Sforza. Ludovico’s court famously supported Leonardo da Vinci, who worked in Milan on projects including The Last Supper.
A common mix-up is Florence, which was strongly associated with the Medici family, or Venice, which was governed as a republic. The Sforzas also ruled Pesaro and held other territories, but Milan was their principal Renaissance power base.