The Wimbledon semifinalist from Carrara sat in the bar area with his family. The 69th ranked women’s player, a hard-charging right-hander from Rimini, ate in the main dining room with friends. Out in the back garden, the 31st best men’s player in the world, a rising star from Rome, chowed down with his team.

It was Saturday night before the start of the U.S. Open, and Via Della Pace, an East Village trattoria, was buzzing. Three of Italy’s best tennis players — Lorenzo Musetti, Lucia Bronzetti and Flavio Cobolli — were dotted around the space, enjoying a relaxing evening at what has become the Italian players’ cafeteria and lounge each year during the U.S. Open.