I receive multiple requests with several questions asking if Alfama neighborhood is safe.
Most of my live I have lived in Lisbon, more than 20 years.
I know very well the city and its best places around. The tourism has changed a lot the city over the past 10 years. The boom of the tourism in the city over the past decade was overwhelming.

There are plenty of places in Lisbon where to stay, safe and central.
Alfama is one of the most historical areas of the city. Its located around the old Castle of St. Jorge (Castelo de Sao Jorge), on top of the hill.
Alfama is usually considered very safe, during day and night. The only concerning are pickpockets, but they are all over the city (well, all over Europe in fact).

My recommendations of best places to stay in Lisbon are Alfama and Chiado, but also baixa and Avenida Liberdade as well.
There are some other areas to avoid, specially at night.
Some places are busier at night (nightlife), such as Bairro Alto, Cais do Sodre, etc

There are some other safe areas close to downtown (5/10/15min), if you wish to spend less money on accommodation: Carmo, Estrela, Lapa, Av Liberdade.
Enjoy our beautiful city! Stay SAFE! Enjoy Lisbon and Alfama!
Feel free to ask any questions.