We loved the place in Alfama! It is small but has everything that you need. The neighbourhood is amazing; besides the cultural sights there are loads of nice little restaurants, shops and places they play fado music. Going to the centre and barrio alto can be done by the old tram (must do!) or by walking (about 30 min). The area is nice enough to walk so we used to do that.
I would recommend staying here to any couple! Thanks a lot for your hospitality!