Galleria Spada
In this neighborhood of huge, austere palaces, Palazzo Spada strikes an almost frivolous note, with its pretty ornament-encrusted courtyard and its upper stories covered with stuccoes and statues. Although the palazzo houses an impressive collection of Old Master paintings, it's most famous for its trompe-l'oeil garden gallery, a delightful example of the sort of architectural games that rich Romans of the 17th century found irresistible.
Even if you don't go into the gallery, step into the courtyard and look through the glass window of the library to the colonnaded corridor in the adjacent courtyard. You'll see—or seem to see—a statue at the end of a 26-foot-long gallery, seemingly quadrupled in depth in a sort of optical telescope that takes Renaissance's art of perspective to another level. In fact the distance is an illusion: the corridor grows progressively narrower and the columns progressively smaller as they near a statue, which is just 2 feet tall. The Baroque period is known for its special effects, and this is rightly one of the most famous. Borromini was responsible for the ruse, but it was only made possible thanks to the careful mathematical calculations completed by a science-minded Augustinian priest Giovanni Maria da Bitonto.
Upstairs is a seignorial picture gallery with the paintings shown as they would have been: hung one over the next clear to the ceiling. Outstanding works include Brueghel's Landscape with Windmills, Titian's Musician, and Andrea del Sarto's Visitation. Look for the fact sheets that have descriptive notes about the objects in each room.