Recent renovations have given a 15th-century palace a contemporary slant, with a flower-filled terraced garden and glassed-in atriums. In the bright guest rooms, stone walls and wood beams offset the modern furnishings and tiled baths. The name refers to Clare (Sorella Luna), the follower of St. Francis whose church is on the other end of town. The Basilica di San Francisco is just down the street.