The neighbourhoods, in local language the “barrios” are all very different, and each with its own ups and downs, good and bad.
In short, Ciutat Vella (Catalan for old city) is made up of
Barceloneta: the barrio next to the beach, originally the fisherman’s barrio, many cool little bars, local feel, a lot of thief and drunks, might be the next up and coming barrio for fancy apartments, a lot of south american immigrants, not so fancy, a bit rough, narrow lanes with fragrant laundry hanging from the balcony and closer to the beach there are overpriced fish restaurants
Born: the super famous and much visited Catedral Santa Maria del Mar is here, also the Picasso museum, beautiful narrow lanes, fancy little shops, little cute bars, top area for reformed apartments for tourists, manicured, nice, posh
Gotico: the most touristy of them all, little cute squares with nice restaurants, many shops, high street shopping, label shopping, gentrified, a bit boring, comfortable, McDonalds, H&M, at night many seedy/touristy bars
Raval: The most young, hip and trendy one; think creative, skaters, graffiti, media folk, Apple products mixing with prostitutes, criminals, drug addicts/sellers and poor immigrants. To me; the most interesting one at the moment. Government trying to “clean up” so it’s changing rapidly. Home to trendy bars and restaurants, the museum MACBA, the cool street Joaqin Costa with vintage shops, bars and restaurants. This barrio is the most densely populated area in Europe, with people from all over the world.
Then there is Eixample connecting the old city with what used to be villages outside the city but have now grown together and forms part of the modern city of Barcelona. For example Gracia, local neighbourhood with lots of buzzing local life and many cute squares and less tourists.
Example is more modern, spacious and fresh than the old city, and has some great restaurants, bars and more upmarket shopping.
Higher up the mountain Tibidabo there’s an old theme park, beautiful to visit, and to see the whole city below.
I recommend Woody Allen’s “Vicky Christina Barcelona” if you haven’t seen it!
Oh and AVOID Las Ramblas, the main street in the city! Full of thiefs and awful food and overpriced bad coffee and sangria!!