SEEN ON THE SCENE: Adam Lambert had his fans buzzing the other night when they spotted him hanging out at the Library Bar at the Public Hotel on the Gold Coast. … Speaking of music men, Grammy winner and actor Coolio slipped into Harry Caray’s Steakhouse in Rosemont to enjoy a bit of calamari and happily posed with the Harry statue on his way out. The “Gangsta’s Paradise” rapper was in  town for a Halloween gig. … Jesse Spencer of “Chicago Fire” was spotted dining at Bar Siena with his girlfriend and his mom — and had such a good time, he came back the next night! … Christie Hefner was seen celebrating mutual birthdays with a few friends at Pomp & Circumstance on North Wells. … Recent sightings at Chicago Cut Steakhouse have been the DJ and singer Shaggy (“It Wasn’t Me”), joined by a nine-person posse — plus (separately) the Cubs’ Kyle Schwarber and country superstar Luke Bryan. … One of the newer entries in the local steakery sweepstakes: STK Chicago recently was checked out by the Blackhawks’ Teuvo Teravainen and Viktor Svedberg. Ditto for the indie rockers the Cults. … Chicago Archbishop Blaise Cupich was spotted quietly attending the closing night of the 51st annual Chicago International Film Festival — screening the fest’s final film: “Spotlight,” which is about the Boston Globe’s expose of the Roman Catholic Church’s cover-up of sexual abuse by priests.