Cory Booker can be frugal and still have a fun dating life. On Saturday, four days into his highly publicized “Food Stamp Challenge” campaign, the Newark mayor was spotted on a date at Bowlmor Lanes by Union Square. We’re told Booker, whose challenge gives him a weekly food allowance of $30, was spotted out with a woman named Diane. “They did not order any food, drinks or even water during their evening,” says a spy. “But they were flirting up a storm.” They stayed about 2 1/2 hours, according to the onlooker, who adds, “He bowled an impressive 151, while Diane scored a 79 in the first game.” Booker’s reps had no comment.