After seeing all the viewpoints in Lisbon, this is by far the best one since you can view the city, the bridge, AND the castle in one place. A bit of an uphill hike bit totally worth it!
One of the most beautiful views of the city. Watch the whole city center, from the Castelo de Sao Jorgeto the Ponte 25 de Abril. Take tram 28 and get off at Rua Graça. Follow the signs 'Miradouro'.
The highest miradouro: a perfect place to watch the horizon. If you want to stay there drinking/eating something, remember to buy it before to go up: on the hill there are just nature and silence!
Out of all the view points I've been to in Lisbon, this is definitely the best one. You can see the whole city from up here. Also, you have a shade here, so don't worry about the heat or sun.
If you want to feel like a real "alfacinha" you must go first to Travessa do Monte, buy a cold beer and a few "tramoços"and eat them while enjoying the best view of Lisbon at the end of the day