Upon my arrival to Lisbon coming out of the subway I quickly identified the potential in the mountain high fort overlooking the Lisbon old city central area. The following morning, I looked it up, and made my way up to see the Castelo de Sao Jorge (São Jorge Castle), a Moorish castle dating back over 2000 years (~48BC, some say 6th century BC). The panoramic views from the top are absolutely spectacular in every direction, and the more recent 11th century fortifications are intact and impressive. The castle basically tells the entire history of Lisbon and gives a good overview of the geographical importance of its location.
It’s quite a hike up the hill, but Lisbon is famous for its elevators system, and so you can easily find the elevator to go up and save you the effort. There’s lots to see and do up there, with impressive demos and a few galleries, and you can easily spend 2-3 hours exploring these vast fortifications and the nearby areas.
Not to be missed when visiting Lisbon. I would actually recommend this is the first thing you do if the weather is nice to give you a good intro to the area. It can be combined with the nearby National Pantheon.