When you don´t have too much luggage (getting up with it to the 4th floor can be heavy) I can highly recommend this fancy apartment in a wonderful neighbourhood.
It´s clean, has got a washing machine and a nice view. And you´re close to the centre. But in Lisbon centre is a very relative term.
If you want a inside tour through the Alfama and it´s history off the beaten tracks visit Gabriela in the Rua dos Remedios (about 100m from the apartment, she runs a small shop where she sells wonderful self-made scarves) and ask for guidance.