Alfama is a very quaint area of Lisbon. It's hilly, has a bohemian feel, and lots of yummy eateries without taking too much out of your pocket. And wear your sensible shoes.
I find going down hill on foot all the way to Rossio, the main city square, is a breeze walk of about 20 mins. On the way back uphill I used tram no 12 from Praca de Figueira and get off just before Portas do Sol. It's less passengers on it than that on no 28.
Benjamin is a thoughtful and kind host and he gave plenty of suggestions. His apartment is clean & comfortable & for me (a solo traveler) has got everything I need & the WiFi is fast & reliable. And I still managed to have a wonderful time Lisbon in spite of the weather.
The description given regarding the area & the stairs going to the apartment are just about spot on.