The small island of Iraklia does not have a museum. If you are interested in history and ancient sites, you can visit the remains of a Medieval Castle on the hill of Livadia, on the eastern side of the island. Of much interest would also be a visit to the cave of Saint John, on the southern side of Iraklia, close to Panagia village. This cave has wonderful formations of stalactites and stalagmites and can be reached on foot.
More museums can be found on the neighboring island of Naxos, one of the most popular Cycladic islands. Naxos is daily connected by ferry to Iraklia and is rich in museums. In Chora, you can visit the Archaeological Museum with exhibits found during excavations all over the island. Also, the Ancient Town Museum is a visit to the excavating site of the ancient town of Naxos.