Sintra is just an hour away from Lisbon by train (leave from the Rossio station), and is where the kings of Portugal had their summer homes. It is cooler and greener than Lisbon, and has several attractions (three palaces or castles). My favorite of these is the Palacio da Pena.
Pena is at the top of a mountain , and is a long, vigorous walk from the train station. Most people take a taxi, and I would recommend this highly unless you are in shape for a two-hour hike up a switchbacked road.
The palace at the top of this road is very interesting for its varied architecture--sort of a blend of Moorish, Gothic, Manueline, and Bavarian. It is considered one of the finest examples of Portuguese Romantic architecture.
Built in the mid-19th century, under the direction of the King Consort Dom Fernando II (of Saxe Coburg-Gotha, hence the Bavarian influence), the palace is still furnished and is quite interesting to visit. The views are also breathtaking.