We had an incredible stay in the Alfama district at Joana's place. I have stayed in many Airbnbs and it is one of the nicest units I have stayed in. We stayed with another couple and it was the perfect size for the four of us.
The neighborhood is perfect for sightseeing and getting a feel for old Lisbon. We did a tuk-tuk tour and I recommend this to understand what you are seeing. Otherwise it's all beautiful but you won't know the significance of things you are walking by.
Some other tips: skip the expensive Fado restaurant directly behind the building (down the stairs). We found much better Fado places just walking around at night. You want to go somewhere a bit more run-down and edgy for that. A couple of great places we ate: the pizza place right next door is AMAZING!! And the nearby Brunch Cafe (that's its name) was the best for breakfast - we went twice, it was so good.
The only downside was the noisy drunken neighbors upstairs who stomped around on the floor at 4am.