Algarve, amazing coastline. Try to explore lots of it. Between Praia da Oura and Albufeira is a great walk across the sandstone rocks, mind your step. Go to the ‘end of the world’ point at Cabo Sao Vicente. When you stand at that last light house on the south western most corner of mainland Europe, you can see why back in the day when not the whole world was discovered yet, they thought that that must have been the end of the world. Left and right of you all you can see, is vast stretches of water, all the way tot the horizon.
Alvor you can stay at Clube Brisamar, a big holiday park, about 2 km from the beach, which has out of season very reasonable prices, especially via booking.com. Go for a gyrocopter flight from Alvor airfield.
Praia da Rocha also great to walk on the beach along the amazing rocks. Just beware of tide coming in, and get back before the beach walk to the stair case is covered with water.
Ilha de Tariva, little sand-island in front of the Algarve coast.
Monchique, a mountain inland in the Algarve.
Lisbon, castle / ruins up on the hills, Belem tower, have the pasteis de Belem (best at the original store at Belem named Pasteis de Belem, but you can get similar pastry filled with creamy pudding elsewhere without waiting in line for a long time), tram, Sintra is nearby with the moorish castle and ruins. Try to pronounce the name of the Discoveries monument in Portuguese (Des Doscribimentos). Our English speaking navigation had quite a bit of trouble with it when we ended up on a road named after it, with a lot of round-abouts / traffic circles. Before every round-about, it said it twice, and on the round-about another time.
Évora, very old town with ruins from a Roman temple from the 2nd century.
Tomar, Convento do Christo, old convent and monastery that has been well preserved
Porto, harbor town, beautiful mosaics / tiles on the outside of buildings
Eat and drink: Portugal has great fresh seafood, also try a spicy chicken piri piri, and as an aperitif: port in Porto