There’s plenty to do in Lisbon itself, of course. In fact you could spend several days without leaving the confines of the city. That said, as residents of this part of Portugal, there are also a lot more things to check out in the area.
A good day trip from Lisbon is to Sintra. There are lots of sights to see including the National Palace at the foot of the hill, the Pena Palace and its surrounding Park and of course the town of Sintra itself. The Castle of the Moors is popular, but we suggest just taking in the views from above and below. A ticket to Pena Palace also gets you into the gardens, Moors’ Castle and the less visited Chalet of Countless Edla. Buy tickets in advance to skip at least one line. Also, at the bottom of the hill just outside of town is the Quinta da Regaleira.
The whole area around Sintra is known as the Sintra-Cascais Natural Park. It includes miles and miles of gorgeous coastline and beaches including Guincho, Cabo da Roca (the westernmost point in continental Europe, Praia da Ursa and other beaches we explored along the coast which you can read about here. You’ll need a car to explore it. If you have one, we suggest driving up the coast for lunch in Azenhas do Mar. And of course, we have lots of good to say about Cascais itself where we make our European home. Both Cascais and Sintra are a quick train ride from Lisbon, though those are two different trains and there is not one in between the two towns, though you can catch a bus from one to the other. That said, each area is worth a day of exploration, so it is best to break them up into two days (but we are biased of course).
To the south, on the Setubal peninsula are many great wineries (not to mention the cheese in Azeitao) which dominate the Lisboa wine region. If you don’t want to explore far afield from Lisbon but want to get into some wine country, this is a good option across the Ponte de 25 de Abril. Closer to Lisbon and near Cascais and Sintra you can also explore the Colares Wine Collective and the cool town of Colares near Praia Grande and Praia Adega.