Probably the best sight to see in Lisbon is the old buildings at Belem. They have even been made a UNESCO World Heritage Site. Most of Lisbon was destroyed in the 1755 earthquake, and the surviving old buildings in the centre were rebuilt afterwards. But not a few miles up the river at Belem. Belem was the port from which most of the great Portuguese voyages of discovery and conquest set out. The main sights are the Tower of Belem, which was a fortress built in the middle of the river (and now very near the shore).
There's also a big quasi-fascist monument to the navigators.
But the most spectacular building is the monastery there, which includes the tomb of Vasco da Gama. One of the things that surprised me most was the fact that everywhere gave me a full student discount using only my University of Oxford card.