Located in the oldest brick house in L.A. (the Pelanconi House, circa 1855) in the oldest part of downtown (Olvera Street), Casa La Golondrina Mexican Café is proud of its touristy status, especially when the authentic Mexican vibe matches the authentic cuisine. And the locals don’t mind, particularly when they’re splitting a pitcher of margaritas and being serenaded by a roaming mariachi band. (Maybe not, if they’re here during breakfast and having a bowl of hangover-nursing menudo.) Tacos and burritos you can get anywhere. And this being a traveler’s spot, there are other restaurants competing for your taste buds. So stick with the house specialties, whether it’s the chicken smothered in chocolate mole sauce, pork baked in banana leaves or crab chile relleno.