While Renaissance-era Gubbio was under the fairly benevolent ducal rule of nearby Urbino, Duke Frederico di Montefeltro commissioned Francesco di Giorgio Martini to build him this palace in the 1470s. Although the sumptuous decorations have mostly been stripped away -- the entire studio of intarsia wood paneling was moved to New York's Metropolitan Museum of Art -- a few furnishings, painted ceilings, and simple terra-cotta flooring survive. You enter through a stunning Renaissance courtyard of pink brick accented in gray pietra serena. Past the ticket booth, a spiral staircase leads down to foundations of the structures that stood on this site as long ago as the 10th century, along with countless ceramic shards. The ground-floor rooms are hung with permanent exhibits, primarily paintings ranging from 16th-century portraits to landscapes of the 17th century. The vast Salone di Corte contains an intriguing holographic installation featuring an actor playing Duke Frederico, but there's nothing labeled in English.

Farther down Via Montefeltro at Via della Cattedrale, a portcullis gate leads into the Piano Voltone, the palace's hanging gardens, open in summer. Snacks and drinks are provided by Snack Bar Giardini Pensili (pizza slices 2€; focaccia 3.50€), and there are dazzling views over medieval Gubbio to the valley floor.