Probably the more interesting historically of the two Bar museums Micklegate contains scale models of battles that Henry VII was involved in. There are also larger scale models of the main characters involved in the information about the main characters involved in the Wars of the Roses. Very knowledgeable and enthusiastic staff.
A combined ticket with the King Richard III Experience at Monk Bar makes this definitely worth visiting combined with the (free) wall walk which will take you around half the city and provide you with good views of the cathedral.