In this 15th-century palazzo right in the center of town, the salons and high-ceilinged guest rooms, a few frescoed and paneled, are reminders of Cortona’s long past as a prosperous and noble town. Tile-floored rooms are appealingly furnished in what might be described as “fading grandeur” style. Some have views over the valley below, while a choice few, including tower suites, have their own terraces. A roof terrace with the same vistas is open to all guests, as is a decidedly medieval-looking courtyard. The San Michele also operates Residence Borgo San Pietro (tel. 0575/612-402), 4km (2 1/2 miles) outside town in San Pietro a Cegliolo, with a countrified take on grand living—14 rooms and 5 apartments set amid 7 acres of olive trees and lavender, with a swimming pool.