I have not yet visited, but want to mention the Likouros Apartments (tel. 27240/51-297), just out of town, which opened in 2009, with five units with TV, electric kettle, and minifridges. I'd call these accommodations more rooms than apartments, but an archaeologist friend who stayed there was pleased with her room, the management, and the view toward the site, and found it much quieter than my old standby, the Pension Zeus ; doubles from 60€.
Note: This information was accurate when it was published, but can change without notice. Please be sure to confirm all rates and details directly with the companies in question before planning your trip.