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.

“It’s beautiful place for us to come,” said Mr. Cobolli, decked out in a crisp blue dinner jacket with a bright white polo shirt underneath. “We always have a table and we eat well, with real Italian pasta.”

Players from other countries also find their spots in New York during the Open. Some French players frequent Le Baratin in the West Village, while others visit Tao’s various locations or the Odeon. But for the Italians, it’s Via Della Pace, where Italian films are shown in silence on the TV behind the bar and memorabilia of calcio (soccer) and tennis adorn the walls.

On any given night during the three weeks of the Open — including a week of practice — there could be as many as five Italian players in the joint, sometimes more, in addition to coaches, agents, friends and family. Matteo Berrettini, who reached the Open semifinal in 2019, fueled up on Via Della Pace’s pasta, is a regular. He sometimes goes several nights in a row.