Britain’s first art school was founded in 1768 and relocated here to Burlington House, a Palladian-style mansion that now has a splendid courtyard in which to enjoy a coffee away from Piccadilly’s fumes and an exclusive new restaurant, the Keeper’s House. A few of its 18th-century state rooms, the six John Madejski Fine Rooms, can be seen on tours. (Charles Darwin’s Origin of the Species papers were delivered for the first time in the Reynolds Room on July 1, 1858.) The meat, really, is on the third floor. First, that’s where to find Michelangelo’s only marble sculpture in Britain, an unfinished circular relief of Mary with the babies Jesus and John. The other attraction is whatever crowd-pleasing paid exhibition is on—always something impeccably selected, such as David Hockney or Australian art. The biggest event is the annual Summer Exhibition, which since the late 1700s has displayed the best works, submitted anonymously; careers have been made by it. A podcast series zeroes in on works at Don’t miss the wooden red “Phone Box No. 1” tucked behind the front gate—it was the 1924 prototype for what we now recognize as an international icon.