North Miami Beach's St. Bernard de Clairvaux Church is the oldest building in the Western Hemisphere. Of course, like every other thing in North Miami Beach, it didn't start off life there. It just retired there. It was built in Segovia, Spain in the 12th Century. It sat there until 1925, until William Randolph Hearst literally ran out of ideas of what to do with all his money, bought the building and shipped it to New York. Then, whoops, the '30s happened so the pieces of the church sat in storage until 1952. Raymond Moss and William Edgemon purchased the parts in 1952, and reassembled them in North Miami Beach.
Today the building is used as an Episcopal church, and is probably the most famous Episcopalian in Miami aside from Albert Cutié. [image and info via Wikipedia