"They were really friendly" one of the managers at Ichiban tells PEOPLE of their dinner. "They just walked in, sat down, and the word started going around that they were here."
The couple didn't ask for a private room or special treatment. "They each had a Hibachi meal and some sushi," the manager says. "The kitchen crew and wait staff were excited to see them. Some of them stayed late because they were hoping to get their picture."
Greene and Jonas didn't disappoint: They posed for pictures, and within hours, the pictures were posted on blogs and Facebook pages.
"I don't watch the Twilight movies, so I wasn't so familiar with them," the manager says. "But everyone else in the restaurant knew who they were." Greene and Jonas were "definitely there together, as a couple," the manager says. "I have to say, they were very nice. I think they'll come back."
Greene and Jonas are in Baton Rouge, where the actress is shooting Breaking Dawn. The cast is expected to continue filming for about two more weeks.