I've included "Herakleidon Museum" in both my lists of museums and galleries, since it's a hybrid between the two. However, I thought I should empasize more the "traveller-friendly" character of this small-yet-significant private museum and the need of including it in your travel plans when visiting Athens.
First of all, the exhibitions here last longer than in any other Greek museum. Practically, it's one exhibit per year, so you can easily plan ahead since you'll know what will be on display 5 or 6 months down the road.
Most exhibitions hosted here present the work of internationally renowned artists (Edgar Degas, M.C. Escher, Toulouse-Lautrec, Edvard Munch, Carol Wax are some of the artists whose work was presented in recent years). I'm not saying that fame necessarily makes one artist better than the other, but most visitors will certainly find more interest and will feel more inclined to visit in these cases.
Great location! It sits in a pedestrian friendly area (Herakleidon St. itself, which lends its name to the Museum, is pedestrianized), close to the grand pedestrian walk of Dionysiou Areopagitou & Apostolou Pavlou, with the Acropolis in view once you step out of its doors. The entrances to the Ancient Agora, the Acropolis and the Acropolis Museum are within walking distance. Plus, it has great access to the Metro network with Thission Metro Station (Line 1) being only 400m away, while Monastiraki Station (Line 1) and Acropolis Station (Line 2) are a slightly longer but pleasant walk away.
It's not a vast place. One hour should be enough for the casual visitor to see whatever exhibit is on display. The building itself is a beautiful 19th century neo-classical mansion with an atrium. You can read more about it (and feel the owners' sense of pride) in the Museum's official website. Last but not least, it has a neat little store, where you can buy posters, games, clothing accessories, cards and other memorabilia from past and current exhibitions.
The exhibition currently on display draws from the Museum's permanent collection. I imagine it's the Museum's way of coping with the economic crisis but you won't feel short-changed in any way if you pay a visit, as it comprises of original works by Hungarian-French op-art leader Victor Vasarely and Dutch master-illusionist M.C. Escher. The common thread uniting these two is the relation between "art and mathematics", which is also the title of the exhibition. A 2-hour lecture and tour of the exhibition, in English, is provided by the museum upon request. Details on opening hours, admission fees, current exhibition, etc. can be found here (mid-page).