Walk around Belem (see the CCB, the monument Padrao dos Descobrimentos, walk by the River Tejo etc) and eat custard tarts (Pasteis de Belem) at the famous cafe Antiga Confeitaria Belem
2. Gulbenkian Museum and Museum of Modern Art
Go to the Gulbenkian Museum and Museum of Modern Art both situated in a lovely garden which is worth a walk around and to sit and relax
3.Catch Tram 28 from Estrela Garden to Alfama
Old fashioned tram is famous and it is wonderful tour through Lisbon (Garden Estrela is near where we live and it is a wonderful park that is worth spending a few hours hanging out on a picnic blanket ...reading or drinking wine!)
4. Watch the sun set with a bottle of beer at a view point... there are a few dotted around the city but I recommend either
Largo da Graca (if you are in Alfama) there is a great view and a lovely cafe
Miradouro Alcantara ( this is near Bairro Alto and Principle Real...good places for bars and restaurants). There is a cafe but nice to buy a beer and sit on a bench!
5. Go to the Oceanario
This is not everyones cup of tea but I loved it. The Oceanario is the biggest Aquarium in Europe and its fantastic. It is also interesting to visit this area which is Eastern Lisbon, the Oceanario is situated in the Parques das Nacoes which is a modern part of the city built in 1998 for the Expo98.
(6. I cheated!! Listen to Fado music in Alfama...we can take you to a little bar...also best pizza ever down the road)