This was my favourite hangout spot in the city. This is the Miradouro Sophia de Mello.
The view of Lisbon from here is stunning, and since it faces West so you can catch the sunset. There is a great outdoor cafe where you can get espresso, beer, wine, snacks. There are plenty of options. It is a great place to relax or socialize. Pretty sure the cafe was a government run establishment and so the prices were very affordable. The Miradouro Sophia de Mello as you can see draws quite a crowd morning, in the afternoon and into the early evening. It is really a great spot to be in the afternoon since the trees offer some shade from the sun which can be intense during summer months.
At about 35 seconds into the video you can see across the way another amazing green spot to spend some time, the Miradouro / Jardim de São Pedro de Alcântara. You can also make your way to the nearby Miradouro da Senhora do Monte for another vantage point of Lisbon.
Here is a good view of the entire length of the viewpoint.