Illustrations taken from the Astor Club Lounge Menu . The Astor Club is a private dining club that offers private memberships as well as reservations for weekly Chefs Table for the general public. The Astor Club is located at 24 Goethe St. in Chicago's Gold Coast neighborhood. The club was originally Maxim's , an outpost of the Maxim's de Paris , one of the most famous restaurants in Paris.