The collection of coins here, dating from ancient through to modern times, is excellent, but of more general interest is the dazzling 1881 mansion in which it's housed. Built by architect Ernst Ziller, it was the home of Heinrich Schliemann, the archaeologist who excavated Troy; fittingly, its mosaic floors and painted walls and ceilings are covered in classical motifs.
The adjoining gardens have an excellent cafe (9am to midnight daily).
A joint ticket for €15 (€8 for students) covers here, the National Archeological Museum, Epigraphical Museum and the Byzantine & Christian Museum, and is valid for three days.