Shia LaBeouf and Carey Mulligan
12/17/2009 AT 02:55 PM EST
and his Golden Globe-nominated
girlfriend, Brit Carey Mulligan
, have been sightseeing in Los Angeles together ... by bus! The two were spotted smooching at a local bus stop by the actor's Sherman Oaks house – and an eyewitness tells us, "Shia has been taking Carey to all of his favorite spots." Among their stops: Lunch at Mexican restaurant Baja Fresh followed by a visit to Borders. "They are a very sweet couple," the eyewitness says. "They browsed several books and would not let go of each other's hands." The two left with a "make your own volcano kit" and finished their afternoon with a movie at the Arclight before strolling home in the dark.