Bernardo e Ana Rita's place is perfect. It is located very centrally and all places are in walking distance. The apartment is very traditional and spacious. It's bright and the temperature naturally adjusts if the windows are opened which is very nice as not even an ac is needed (even though an ac still can be usedin every room). I can recommend staying in the apartment.
Ps: Close by is a very tasy breakfast place called Dear breakfast - alfama which is great for a nice morning brunch.