With its opulent fountains, theater and large thermal baths, Hadrian’s villa in Tivoli, Italy, was a fitting setting for the second-century Roman emperor to welcome guests, host parties and commemorate battle victories.

Centuries later, it’s the mundane—not the magnificent—details of the 300-acre complex causing a stir, as Columbia University researchers and students digging on the Unesco World Heritage site uncover new sections of the villa that offer a rare glimpse of ordinary life in ancient Rome.

“There’s...