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Lisbon's seven hills define the day. The city was rebuilt after the 1755 earthquake on a grid (the Pombaline Baixa), but the surrounding neighbourhoods kept their medieval lanes and dramatic gradients. Tram 28 loops through Graça, Alfama, Baixa and Estrela in about 50 minutes, the easiest way to cover the centre without climbing. Catch it at Martim Moniz (the eastern terminus) early in the morning. By mid-morning the queue runs 30+ minutes and the tram is too crowded to enjoy. The Bica, Glória and Lavra funiculars handle the steeper climbs, all covered by the 24-hour Carris pass.

The Castelo de São Jorge sits on Lisbon's highest hill with a 360-degree view across the Tagus estuary, the 25 de Abril Bridge (Lisbon's red Golden Gate twin) and the Cristo Rei statue on the south bank. The walls and battlements are 11th-century Moorish; the Alcáçova tower is the photogenic peak. The Sé Cathedral (12th century, the city's oldest church) and the Roman theatre ruins sit at the foot of the castle hill in Alfama. Alfama itself is the most atmospheric neighbourhood: tiled facades, narrow stone stairways, the Miradouro de Santa Luzia viewpoint and the Igreja de Santo Estêvão belltower.