After breakfast at cafe Ferrari we hiked up the hill to our east where we spent the morning exploring the remains of Castelo de S. Jorge, the 11th century Moorish castle that overlooks the city and the water. It's pretty well preserved and worth seeing, though not nearly as interesting as Marvao's castle.
From the castle we wandered the streets that lead down to the water then we headed west and explored the Chiado and the Bairro Alto neighborhoods. They offered charming streets with cafes, roasted chestnuts, and street musicians.