Potsdam really rose from World War II ashes only in the last decade. Most of the old city centre has been rebuilt, historically accurate though with modern materials. The Barberini is an excellent, slightly posh addition, along the water and within walking distance of the railway station.
It features modern art, with mostly temporary exhibitions. The three floors feature spacious rooms that can host medium-sized exhibitions. Cutting-edge it isn’t, but they usually provide good overview shows of modern art.