Star watch: Anthony Rizzo, Billy Corgan, Emmy Rossum, Judd Apatow

SEEN ON THE SCENE: Things were REALLY hopping at Bub City the other night when country music star Brett Eldredge (in town for the CBS/US99 “Stars & Strings” concert) hopped on stage to perform one of his hits with the band — and then was joined by World Series champ Anthony Rizzo to perform “Go Cubs Go!” … No singing was involved, but Food Network mainstay Anne Burrell was also sighted recently at Bub City. … Speaking of the Cubbies, rocker Billy Corgan, one of the team’s biggest fans (and that’s a huge legion of folks!), was spied dining at Harry Caray’s Italian Steakhouse in Rosemont. … And the Cubs’ Justin Grimm visited Sullivan’s Steakhouse in Naperville. … Meanwhile, onetime heartthrob Chad Michael Murray made the scene at Harry Caray’s Tavern on Navy Pier, while here for the “One Tree Hill” reunion at EyeCon. … Also seen separately at Harry Caray’s Navy Pier outpost was Cubs outfielder Albert Almora, Jr., joined by his family. … “Shameless” star Emmy Rossum has become quite the regular at both Beatrix River North and the Beatrix in Streeterville. … Recently RPM Steak sightings have included Dwyane Wade, Jamie Gray Hyder (“True Blood”), rapper Lil Jon, and Cubs hero Kyle Schwarber. … The cast of “Hamilton” made the rounds the other night — dining at RPM Italian, having drinks at Ramen-san, before rounding out the night at Three Dots and a Dash. … Also seen by fans at RPM Italian was award-winning comedy producer/writer Judd Apatow and his hilarious actress wife Leslie Mann, while here for parents weekend at Northwestern, where their daughter is a student. … It’s a huge week for Chicago-based, Tony Award-winning producer Mary Lu Roffe, who has two shows opening in the Big Apple this week. “Natasha, Pierre and the Great Comet of 1812,” starring Josh Groban, opens Monday on Broadway; and “Othello the Remix” (which originally was a huge sold-old hit at Chicago Shakespeare Theatre) opens off-Broadway at the Westside Theatre on Wednesday. … Wyclef Jean performed at The Bassment Saturday night — at an event for the Remy Producers Series, a competition between the hottest up-and-coming music producers in town.