The small island of Mathraki has no museums but the closest ones will be found in the neighboring island of Corfu, which is linked to Mathraki by boat from Corfu Town, Sidari or Agios Stefanos. Corfu, in particular, has a lot of interesting sites and museums. Especially Corfu Town is an awesome place for sightseeing.
It has plenty of museums, such as the Archaeological Museum in Garitsa Bay, the Museum of Asian Art in the Palace of Saint George, the Byzantine Museum in the church of Antivouniotissa and many other smaller-scale museums with valuable exhibits.
Corfu also has many historical sites to visit, such as the two fortresses in Corfu Town, the amazing Angelokastro in Paleokastritsa, Achillion Palace in Gastouri, Kassiopi Tower, the Shipyards in Gouvia and other places, less impressive but very interesting.