The apartment we stayed in was right in the heart of everything and made a great home base for walking to the main attractions in central Barcelona. Though it was in a busy area, it was relatively quiet at night and the morning sunrises were lovely. There is a nice fruit market vey close by and some convenience stores right below.
The area is probably not the safest in all of Barcelona, my daughters and I frequently had weird vibes from some of the men who seemed to be just loitering in the nearby streets - this was especially true after dark. It would be wise for everyone to be very aware of this if choosing to stay in this apartment. The biggest complaint/frustration was that on our second night there, we were woken up at 3:30 am by insistent ringing of our door buzzer. Someone had complained of noise coming from our apartment - which was not true, we were all sleeping. It unsettled all of us.
And, as others have mentioned, the flat is up 5 flights of stairs - know this!!