Rather, Alec Baldwin stayed put in his seat during his visit to The Late Show with David Letterman (well, before he tossed around a pig skin with Dave and football legend Joe Namath), to properly introduce his girlfriend, 27-year-old yoga instructor Hilaria Thomas. After delving into talk that he’s contemplating running for mayor of New York City, Baldwin — who joked “I would like to be the mayor, I don’t know if I want to run for mayor” — said his 30 Rock schedule and personal life could alter that. Baldwin later introduced Thomas, who waved shyly from the green room. Alec Baldwin wants to concentrate on his love life rather than his political ambitions.