It was a great stay! The hospitality was really excellent. The room was nice, with a great view and during the night silent. I used the bike and cycled along the coastline, what I could really recommend. Sofia helped me with the bike and invited me to the restaurant, where the works. It was a wonderful evening!
From the flat I went with the train to Cascais and took a bus to Sintra, that was easy to organize. In Sintra take the bus for 6,15 Euro (it is a hop-on-hop-of,) and watch at least the Palácio Nacional da Pena, the castle Castelo dos Mouros is not so interesting, it is basically the view. The old city goes along with the Sintra National Palace, both worth to see.
In Cais do Sodre are lockers, if you need some (next to the yellow box, a bit difficult to find, 1,50 Euro for three hours). If you are interested in a wonderful night show, go to "Lisbon under stars". It takes place in the ruin of an old church and illustrates the history of the city with light and other special effects (15 Euro). You have a great view from there also!