If you are staying in Carcavelos, and hiring a car you are well placed to explore North of Lisbon.
You could drive along the Marginal to Estoril and then take the N6-8 to Sintra. See the Pena Palace,etc. Afterwards, take the N247 towards Cabo da Roca (The most westerly point on the European Continent) and then back to Carcavelos via Cascais.
See:
http://en.wikipedia.org/wiki/Sintra
Although the distances are not great, you may find that is enough to do on day 1.
Another day trip could be to visit the old historic walled town of Obidos, and then on to the historic towns of Alconbaça and Batalha
all of which have over he centuries been linked closely to Portuguese and European History.
See these links:
http://en.wikipedia.org/wiki/%C3%93bidos%2C_Portugal
http://en.wikipedia.org/wiki/Batalha
http://en.wikipedia.org/wiki/Alcoba%C3%A7a
Another day trip could be to drive towards Lisbon, cross over the 25 Abril bridge and visit Palmela, Setubal, Alcacer do Sal and then back to Carcavelos.
See:
http://en.wikipedia.org/wiki/Setubal
http://en.wikipedia.org/wiki/Palmela
Coimbra or Nazare are also doable from Carcavelos on day trips but will require at least 2 hours driving each way.
