Nicknamed “the Brain of Veneto,” Padua is home to the prestigious university (founded in 1222) that hosted Galileo, Copernicus, Dante, and Petrarch. Pilgrims know this city for the Basilica of St. Anthony, where the faithful assemble to touch his tomb and marvel at his holy relics. It’s a great place to experience Italy: to make some new friends, get chummy with the winds of its past, and connect with the delights of its now. I start my visit with a ramble around the old town center. It’s a colonnaded, time-travel experience through some of Italy’s most inviting squares, perfect for lingering over an aperitivo. But it’s not stodgy — this university town has 60,000 students and a youthful spirit. No wonder Galileo called his 18 years on the faculty in Padua the best of his life. I see young people — apparently without a lot of private space in their …