There’s a fabulous old town, the Baixa, cascading down a hillside in clusters of tall, narrow, whitewashed buildings. You can walk in the cobbled and even tiled streets there, which in places get so steep that they literally become flights of stairs. Or, just sit back at a café spilling onto the brick-paved Praça do Comercio, the main square, and sip an espresso and nibble on those crumbly custard tarts as you people-watch. But if you go to the top of the hill, in Alta, you'll discover a 13th-century university, the oldest in Portugal, with amazing old buildings and walls adorned with glazed blue-tile murals they call azulejos. And yes, the vista point there, on the edge of campus, Penedo da Saudade, has the best view in the house – clear across the city!