As a couple, Águas Livres Aqueduct works.
A genuinely awe-inducing piece of engineering — colossal pointed arches that survived the 1755 quake intact, with seasonal walks atop the span over the valley. The catch: the walkable section keeps limited hours, it's west of the centre and easy to miss, and from below it's a quick photo. A treat for engineering and history buffs willing to detour.