We rented an apartment in Alfama for 3 weeks on our first visit to PT. It was on a top floor of an old building with a great view of the river - that was the main reason for us to stay there. We did not realize the stairs would be so steep and narrow (our american luggage could only fit sideways up the stairs). On the ground level, there was a Fado club but we had no noise issues.
It was close to Apolonia train/ metro/ ferry station - very convenient location, and there is a grocery in the train station (the most limited Pingo Doce food market as we learned later). It's a walking distance to Plasa de Comercio which is the center of Lisbon.
Another "surprise" was lack of heating elements AT ALL in the apartment. It was Christmas/ NY time, so the owner (or his helper) brought an electric heater and it was almost useless b/c the balcony doors were old and not replaced with newer model (the whole apartment was newly renovated except for that door). We survived as we were out of the apartment most of the day walking thru the neighborhood - those hills will warm you up in no time! At night, we piled all blankets and coats over. So, we mostly ran the electrical heater by the bathroom door to warm it up before the shower (water pressure and temperature was good) . As all utilities were included, we had no idea about the cost but no doubt that electrical bill was huge. So keep the heating on the list of your living expenses. We learned later that the best way to arrange your house heating system is to install the heating elements under the floors. Next time, we stayed in the apartment with heated floors and it was very comfortable (in February).
We had no neighbors to interact, but saw lots of Brits out in the neighborhood and in the local cafes. They were not very social... We had a friendly interaction with a person running the local P.O. next door to ours - actually, next porch, as we lived in a very long and old apartment building with lots of doors of different colors. The post office person helped us with some certified envelope forms, he and his wife somehow knew that we lived in the same building, they both spoke decent english and were helpful answering our questions about the local restaurants.
Another positive experience was with our laundry - everybody is hanging it outside the windows, so did we and one of our underwear items fell down and hang on the TV dish down. We couldn't find out how to reach that neighbor, asked the owner for help - nobody was present at the place until the last day of our stay, when we found our laundry folded in a plastic bag placed right by our entrance door on the 3d floor. We conceded it as a friendly gesture.
The most disliked feature of Alfama for us was trash on the streets - we were instructed by the host to take our plastic bags filled with garbage down to the street and leave them any place (steps, corners, etc). we couldn't believe it and asked the P.O. people and some cafes' owners for confirmation. Yes, there were some city brigades collecting trash driving around, but still it was a very unpleasant sight every day, and it was winter time! can't imagine, how it smells in summer!
Next time, living in a different part of Lisbon and in different suburbs, we got acquainted with the most sophisticated trash collection system in the world! But not in Alfama...
These days, we plan to retire some place near Lisbon, from Belem to Sintra, but have no desire to go back to Alfama.