Ok, this thing's you can' really miss: TRAMWAY 28 give's you the best view of the city: from Martim Moniz to Prazeres, stop's in all important places: s. Jorge castle, bica, alfama, santo antonio church and so on. Lunch/brunch/dinner in any cousy little restaurant in Alfama
DO NOT BUY THE TICKET IN THE TRAMWAY: it's more expensive. Buy 7 colinas in a payshopp agent (any post office in lisbon sell's you one, then you jus't reload it. You can use it to subway also.
In Belém: [take tramway 15 from Praça da Figueira to Dafundo]. In there see Torre de Belém, Mosteiro dos Jerónimos, Padrão dos Descobrimentos, Centro Cultural de Belém (one of the biggest modern art collection is there). What to eat there: pastéis de belém, you'll see where it is when you go out the tramway!!! Lunch/brunch/dinner in Docas, underneath ponte 25 de Abril, I recommend you Celtiberos (not to expensive and very nice)
Take all the the city offers: Glória (by night: Bairro Alto), Lavra (there take a visit to Torel garden) Bica (nearby you have Brasileira coffe shop, Santa Justa (great view of the city).
Take the train to Sintra (from Rossio station), you'll get there in half an hour, cost's less than 4 € and it's beautiful: see the palace, quinta da regaleira, capuchos and eat TRAVESSEIROS.
Nightlife in Cascais and Estoril is 5 stars.