Around Lisbon there are two places:
Belem--Mosteiro dos Jeronimos and the Torre de Belem.
Sintra--MUST go to Palacio da Pena, and you can get a package deal and get into the Quinta da Regaleira as well which is well worth it.
I would definitely recommend going up to Porto, the 2nd biggest city, and enjoying that for a day or two--the Franciscan church is great there, you can enjoy port wine across the river, and just enjoy the beautiful views. From there you can...