Lisbon is a city built on seven hills, and the trams exist for exactly that reason.
Ride the number 28 tram end to end at least once, ideally early, before the queue for a seat stretches around the block. It rattles through the Alfama's narrow lanes close enough to touch the tiled facades on either side — the best free sightseeing tour the city offers.
Spend a morning getting lost in the Alfama itself on foot, fado drifting out of doorways, then climb to the Miradouro da Senhora do Monte for the widest view over the rooftops down to the Tejo river. Lunch on grilled sardines and a glass of vinho verde somewhere with no view at all — the food is usually better where the tourists are not looking.
Cross to Belem for the custard tarts at the original Pasteis de Belem bakery, still warm and dusted with cinnamon, and the Jeronimos Monastery next door. Close the weekend at a miradouro at sunset with a glass of ginjinha, the sour cherry liqueur sold from tiny hatches all over the old town — Lisbon does its best work in that last hour of light.