Praça do Comércio is simply unmissable. It is a large square with perfect architecture, surrounded by elegant buildings and generously overlooking the river Tagus. Locals also call it by its old name, Terreiro do Paço, or Palace Courtyard, because it used to be the centre of the Portuguese worldwide empire. The royal palace was located in the square for some time, and large trading vessels used to arrive there, bringing precious spices and other colonial goods which were traded for gold. In 1755, Lisbon was hit by a huge earthquake, followed by a fire and a tsunami, which destroyed most of the city centre. The square and the Baixa neighborhoods around it were built anew from the rubble and display today very beautiful façades of tiles and cast-iron balconies.
The Rua Augusta triumphal Arch overlooks the North side of Praça do Comércio in all its magnificence. It is adorned with statues of various historical figures, the coat of arms of Portugal, and a beautiful sculpture representing Glory rewarding Valor (personified by an amazon) and Genius (encompassing a statue of Jupiter). You should absolutely go to the top of the Arch (there is a lift!) and admire great views of the city and river, especially at sunset. The statues will look huge from that perspective, so have some fun, take photos by their giant toes and turn them into very original Instagram posts, hashtag #toe.
Praça do Comércio is also a good starting point for exploring Lisbon on hop-on-hop-off double-decker buses, or simply to have a drink in one of the many outdoor cafés.