Palazzo Madama is a layer-cake of Turin's history: a Roman gate at its core, a medieval castle around it, and Filippo Juvarra's white Baroque facade tacked onto the front in the 1720s. It now houses the Museo Civico d'Arte Antica, with rooms running from medieval sculpture through Renaissance and Baroque painting to the famous Portrait of a Man by Antonello da Messina — one of the most arresting fifteenth-century portraits in Italy.
Even if you skip the museum, climb Juvarra's grand staircase for its sheer theatrical scale, and the tower for one of the best free views over Piazza Castello and the Mole. The cafe on the ground floor is good for a coffee under the original medieval vaults.