For those with cultural yearnings the Hellenic Ministry of Culture's "magic map" is all that's needed to navigate round the island. It breaks down Corfu 's heritage into Museums(seven in total), Archaeological and Byzantine sites and a lamentably uninspiring "Recent Monuments"(complete with sharp images and potted histories). The map can take some getting used to, the graphics are elementary and it takes time to 'discover' what's clickable and what's not. But stick with it, as perseverance pays dividends(the blue spirals seem to access most of the information).
Corfu Town 's Archaeological Museum houses a unique collection of statues and funerary art dating back to the 7th century BC(keep an eye out for the 'Lion of Menecrates' one of the Museum's biggest draws despite resembling a slumbering walrus). The Museum of Asian Art was founded in 1927 after a sole benefactor(Gregorios Manos) donated 10,500 pieces of Chinese and Japanese art to the island. It's since expanded to include private collections from central Asia, and is beautifully housed in another of the Greek royal family's former summer residences.
As for ancient monuments, other than the Old Fort, most of the action is concentrated on Paleopolis - the ancient city of Kerkyra(located in the Mon Repos estate). Alongside the Agora(marketplace) there are several public buildings, sanctuaries, a recently restored Roman bath and a little further afield the dockyards serving Alkinoos harbour. The estate is also home to the honeycombed Church of Saints Jason and Sosipater - although it dates from the 10th century, the frescoes and painted icons that attract the punters weren't added until the 17th century.