Barcelona is a mid-big city which is all contained between sea and mountains and two rivers: Besos and Llobregat. if you come from a flight and you are landing the Areopuerto del Prat you can spot the whole city at the first sight.
This means that Barcelona is a human-size city and is also very well connected by metro and buses.
What do we mean with this?
In Barcelona you will have the feeling that everything is near, as long as you live in the metropolitan area. So our suggestion is to don't worry if you don't find accommodation in the center, you can enjoy the city and move by metro and reach any place in few time.
Where the best to live?
Around the center
The Eixample is where everybody wants to live. Is divided in Eixample Esquerra and Dreta ( in Catalan meas left and right ), but there are other areas that are really good around the center: the area around Marina Metros station, Poble Nou, San Antoni.
Out of the center
Not very centric areas but recommended: Gracia, Les Corts, San Gervasi / Sarria, Vila Olimpica
City center (Historic center):
Considering that the real center is Plaza Catalunya, if you want to live the experience to stay on the rambla or some peculiar old district of Barcelona is also a good choise and is an authentic experience. But mind this pros and contras about living there:
Contras
is noisy
is dirty
is stinky
Vagabonds around
Pickpockets also finding some opportunity around
Pros
You feel in the authentic Barcelona
You see people every time
You can go out every night and day
Shops, bars, restaurants
It make you feel alive
Where is safe?
In general everywhere is quite safe, is very difficult to get involved in some aggression. The main danger in Barcelona are pickpockets.