Cache is just outside the front entrance of the Museum of Byzantine Culture which is one of the finest museums in the world devoted to Byzantine art and civilization. The impressive collection includes many Byzantine and early Christian frescoes, icons and artifacts.
You are looking for a cache that's slightly larger than a 35mm container, so be sure to bring your own pen.
Happy hunting!
Small note on cache maintenance: I regularly visit Greece but in the meantime a local geocacher has kindly offered to assist if any issues arise between my trips.