I receive multiple requests asking if Graça Lisbon area is safe?
I have been living in Lisbon most of my life, at least until university, law school, up to 22 years of age.
I know each corner of the city very well, although the city of Lisbon has been changing a lot recently, with the boom of the tourism in the city over the past decade.

There are plenty of places in Lisbon where to stay, safe and central.
Graça area is a very general safe area, during day and night, although, not my best recommendation to stay in Lisbon. Not exactly walking distance from most atttractions,  but at the same time not far (10-15min driving distance by taxi).

My recommendations  to stay are Alfama or Chiado, although prices can often be more expensive than Graça or others.
Try avoid Intendente, Anjos, and Martim Moniz. Although OK during day period, tourists may not be comfortable walking alone at night. Mouraria although being a very typical neighborhood of Lisbon, and although safe during day, some guests may not feel comfortable as well. Bairro Alto is historical but extremely busy at night. Avoid if your idea is relax and stay quiet, and the same with Cais do Sodré.
 

 
Other safe areas close to downtown (5/10/15min): Baixa, Carmo, Estrela, Lapa, Av Liberdade.
On either place chosen, walk on lighten streets and avoid alleys and dark roads. Use taxi at night.
Enjoy our beautiful city!