The theatre is most likely the Theatre Royal and the rooms referred to here are the Assembly rooms, of which the octagon room (below) is one. The former was for plays and theatricals, the latter for balls, parties, and social elbow-rubbing.
The vanity and social ambition of Miss Elliot and Sir Walter are again revealed in their disdain of the forms of entertainment which are good enough for gentlemen like Captain Wentworth and the Crofts.
Both are still lively venues today. For more about the Theatre Royal, try their official site.