The Bouleuterion lived to see three different period. Rock-cut stairs that are still visible adjacent to the building were once part of the theatron during the first, Hellenistic, period. When the rock formation underneath the theatron collapsed separate tiers of seats were carved to the north of the former seats during the second period. At that time the floor of the orchestra was raised and bordered with rubble stones. Later, the theatron collapsed once again and was repaired again. During that third, Roman era, period the theatron was converted into a rectangular hall with wooden columns placed atop marble bases recycled from older buildings in de city. This hall was erected on the same level as the orchestra, rock-carved by half its size in an east-to-west direction.
Source: Notice on site.

For some reason I keep overlooking this location, but with the help of View Map I can safely say that the stair-like structures in the right lower corner are some of the seats, so the empty space will be the bouleuterion's central space.