To qualify as a Broadway Theatre, the theatre must seat 500 patrons or more, and be located in Manhattan. The Broadway League—the national trade association for the Broadway industry—must also deem the theatre a “Broadway House.”
Broadway.org has an excellent site with a list of all Broadway theatres and the shows that are currently playing—or soon to be playing—at each theatre. A 👏 means that I have seen one or more plays at that theatre.