Respect the hills
Lisbon is built on hills, and underestimating them is the classic first-day mistake. Plan routes that climb once and descend the rest, use the historic trams and funiculars where they help, and keep walking days realistic. The reward is one of Europe's most atmospheric capitals.
Four days works cleanly: two for the central neighborhoods, one for Belém, and one for Sintra, which is too good to skip.
Day 1: Alfama and the castle
Start in Alfama, the oldest quarter — tangled lanes, miradouros (viewpoints) and the Castelo de São Jorge at the top. Ride tram 28 part of the way if your legs are protesting. End with a fado dinner if you want the cliché done well.
Day 2: Baixa, Chiado and Bairro Alto
Walk the grand Baixa grid up to Chiado for coffee and bookshops, then into Bairro Alto, quiet by day and loud by night. Catch sunset from the Miradouro de São Pedro de Alcântara.
Day 3: Belém
Head west to Belém for the Jerónimos Monastery, the Belém Tower and the original pastéis de nata at Pastéis de Belém. It's a half-day of monuments by the river; keep the afternoon loose along the waterfront.
Day 4: Sintra day trip
Take the train to Sintra (about 40 minutes). Pena Palace and Quinta da Regaleira are the highlights — book Pena ahead and go early, because the town fills fast and the hilltop buses crawl by midday. Back in Lisbon for a final dinner.
For another European capital, compare the Barcelona itinerary. For a city where pacing matters as much as sights, see the Rio de Janeiro itinerary.