Go from Rossio Station in Lisbon to Sintra by train
Buy the rover ticket for the Greyhound bus that lets you travel in and beyond Sintra (there is a cheaper one for Sintra only)
Use the local bus to see the town and the National Palace, the Castelo dos Mouros and the extraordinary Pena Palace.
Take a bus from the station at Sintra to Cabo da Roca, the westernmost point of mainland Europe
Take a bus to Cascais (and very possibly eat there)
Return by train to the Cais do Sodre station in Lisbon.
You will need to check bus timetables carefully but both train lines are frequent and cheap. if you return from Cascais after dark (avoid the late-night train, for safety reasons), you will get wonderful views in Belem of the floodlit buildings.
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Lisbon Region Travel Guide from Wikitravel. Many thanks to all Wikitravel contributors. Text is available under Creative Commons Attribution-ShareAlike 3.0, images are available under various licenses, see each image for details.