My wife and I stayed four nights at Ana & Fátima's apartment in the Alfama. They were great hosts, greeting us warmly when we arrived, helping us with tips on where to find a decent restaurant or two in the area, where to get the best transport, and giving us other useful information. When we needed a taxi to get us back down the hill to the train station, they arranged that for us as well. The tram 28 is right outside your door and many interesting sights are within walking distance. I would most definitely recommend staying with them!