As mentioned in the previous post there is an amazing view over Lisbon from the Jardim de São Pedro de Alcântara. You must check out. It is located in the Bairro Alto which is just West of the central downtown part of old Lisbon. There are also many other sites such as the Jardim Botânico da Universidade de Lisboa, cafes, shops, and nightlife to check out on this side of Lisbon.
There are 2 terraces in this garden and the view is stunning looking East at the old town downtown below, and you can also see the walls of Castelo de São Jorge and Lisbon Cathedral to the right and in the distance. Far in the distance is my personal favourite viewpoint in Lisbon, the Miradouro Sophia de Mello.
A great place to take it easy and ponder life. If you go there at sunset you can see the castle and cathedral lit up nicely.
A close up of of Castelo de São Jorge. Lots of colourful red rooftops in Lisbon.
And in the photo below you can see the Lisbon Cathedral. When you make your way over there you can stop and have a beverage just to the side at the Jardim Augusto Rosa.