For our first full day in Lisbon we decided the best way to aquatint ourselves with this massive, fantastic, very hilly town [it seems the only reason you go down a hill is to go up another] was aimlessly wandering. A lot of wandering and a lot of hills.
Many of the touristy parts of Lisbon do not run on a grid [The Baixa being the exception]. It makes determining paths of motion a bit more difficult than plugging it into Google Maps and heading off. There are steep hills, stairways and dead end streets to take into consideration. We quickly learned that the Google Map designation of "mostly flat" meant basically zero.
Some public transportation is helpful. The subway is a bit inconvenient for us. We are staying in Principe Real for two weeks so the most efficient option for us is either walking, the bus or Uber [which is super helpful when your apartment is up a steep hill].
One highlight was making it to Chiado to see the Convento do Carmen or Convent of our Lady of Mount Carmel. Destroyed in the 1755 earthquake that ravaged Lisbon and ended her Golden Age, the remains of the church are now an archaeological museum. While small, having a collection of church artifacts housed under the remains of Gothic church arches with no roof, is quite powerful and interesting.