Scaplens Court and the old Town Cellars are the two best-preserved medieval buildings in Poole, and are located just next to the Museum (in fact the Town Cellars are attached to the Museum itself). The Cellars were a storehouse for the trade goods that came in and out of Poole at this time. In the summer you can enter Scaplens Court to see the reconstructed medieval garden inside.
Both buildings are at Museum Precinct, one of the locations on the Story of Poole trail. Pick up a leaflet at the reception desk to follow the trail into the streets.