Anna Wintour hosted a swanky private party for tennis stud Roger Federer’s 31st birthday at the not-yet-open Beatrice Inn Thursday night. The formal but relaxed affair featured a star-studded guest list, including Diane von FurstenbergOscar de la RentaNicole KidmanKeith UrbanBradley Cooper and Seth Meyers. The evening started with a cocktail hour, followed by dinner. After the meal, coaches Stéphane Vivier and Severin Lüthi served a tennis-theme cake made by Sweet Lisa’s. Wintour, who normally makes a quick appearance at events, stayed until 11 p.m., according to our source, while Federer hung out till midnight with a group of friends. The party marks the first event for the much-anticipated reopening of Graydon Carter’s — along with partners Emil VardaBrett Rasinski and former Per Se chef Brian Nasworthy — steakhouse version of the West 12th Street former underground hot spot. No opening date has been set, but we are told they will be hosting events during Fashion Week. [Page Six]