Lodging in La Conner Katy's Inn is one of the oldest homes in La Conner, and when opened in 1984 was the first bed-and-breakfast in town. The Inn sits high on a hill only two blocks from the beautiful artistic town of La Conner with easy access to sightseeing, shopping and dining. There are three bedrooms upstairs, that all have doors onto the balcony and one bedroom downstairs with a private entrance. All four rooms have private baths.