Eat grilled sardines in the Alfama district, gaze at seemingly endless views, marvel at the impossibly steep terrain and travel, as locals do, by metro, tram and funny funiculars.
Visit the Oceanarium, one of Europe's largest aquariums, and beside it the Knowledge Museum (Pavilhao Conhecimento), a hands-on attraction for all ages from three, where you can moonwalk, barfly jump and blow bubbles. Then check out the Museum of Art, Architecture and Technology (MAAT; Museu de Arte, Arquitetura e Tecnologia).
Seek out the haven that is Principe Real Gardens, with an overhanging canopy of ancient trees and a peaceful café that make this a great place to just hang out. Join the yummy mummies on a Saturday-morning shop before the organic farmers' market.
Check out Lisbon Zoo, with a mini-cable car-ride over the lion enclosure included in the admission price.
Visit the beaches of Sintra. Little known by tourists, this area is well worth a short trip out of the city. Praia de Macas with its great bodyboarding is especially good for families, while Praia Grande is favoured by surfers. Lifeguards are on duty mid-June–mid Sept.
While you're in the area, take a trip to Azenhas do Mar ('Watermills of the Sea'), a whitewashed village trimmed with blue, built on the slopes of the cliff with a river cascading to the sea below and fascinating rock pools. Recently restored, the watermills are now home to a restaurant, bar and swimming pool.