We had a great time staying in Alfama with Ricardo's flat - though the bedroom is very small and with no window inside for ventilation/circulation. We slept in the living room instead and had no problems though there are no blinds, so do bring an eye mask if you need darkness.
Alfama is a wonderful area, and there's a fado bar right outside the flat and an AMAZING bakery right next door. Having said that, the local tube station isn't the most helpful for connections to Sintra/Cascais, and a lot of the main bars/restaurants are a good 25 minute walk away and through a lot of hilly streets and stairs. There is a local bus/tram stop, but if you want the best of both worlds it might be easier if you pick something a bit further West towards the centre. We loved this as we walked everywhere, but be careful if it's not your thing!