We highly recommend Anna's apartment. We stayed there for a month and loved making this our home away from home.
The apartment was just remodeled, so everything is new. The unit is modern, comfortable, and clean.
The unit is in the Alfama district of Lisbon, which is the old town. There is a ton to see and do, but still really quiet. The neighborhood is very hilly, so be prepared to walk some hills.
When I come back to Lisbon, I definitely would stay here again!