I recommend at least 4 days in Sintra.
The first day you can visit Sintra's three most famous landmarks. First of all the Royal Palace is at the center of the village and it shouldn't take you more than an hour. Then you can climb to the Moorish Castle (or take a bus), there isn't much left but the view from the top is worth getting there. Finally you have the romantic Pena Palace and its Park, where you can start a short trek.
Take at least half day to explore the mysterious Quinta da Regaleira. There are so many caves and passages. It's close to the center. Then you can visit by bus Europe's westernmost point, the Cabo da Roca. I also find the place to be quite inspiring.
You shouldn't also miss the Montserrat Park and Palace and specially the Capuchos Convent, a very special place made out of cork and stone where you'll be able to imagine how monks could live in their small cells. Although a bus can take you to Montserrat, no public transport is available for the Cork Convent. You should make an arrangement with a taxi.
And then you have your last day. You can either head to the Queluz Palace by train or have a nice walk at the surrounding forests. Or even go to the beach in summer.