If you go to Lisbon, save 1 day and go to Sintra. You can get there by train within a half hour or 45 minutes and we were able to see 4 sites all in 1 day.
We spent about 8 hours in Sintra and visited Quinta da Regaleira, Convent of the Capuchos (took a taxi there), Palácio Nacional da Pena (this post), and finally the Castle of the Moors from where we walked down the hillside back to Sintra and the train station to head back to Lisbon.
The iconic Pena National Palace was originally built on the Monastery of Nossa Senhora da Pena. During the 18th century the palace was first severely damaged by lightning and shortly thereafter by the earthquake of 1755. It was later acquired in 1838 and renovated extensively over time through the initiative of Ferdinand II of Portugal. The palace is a Romanticist palace and sits high up on a hill above Sintra. On a clear day it can be seen from Lisbon. It is one of Portugal’s most visited monuments.