Apartment location in Barcelona

You shouldn't be worried about safety... Barcelona is quite safe (yet it's a city nonetheless!).

However, while the Old Town has, as you put it, character, some people feel the narrow streets a bit intimidating (and even rowdy) so perhaps the wider streets and avenues of the classy Eixample can feel more natural to certain people.

As per distances, note that the city is fairly compact and has an excellent transportation system. Furthermore, the city -as many other European cities- doesn't have "a" centre and then residential neighbourhoods but "many" centres instead. Barcelona grew up absorbing neighbouring towns -now districts of the city- and each one has it's own 'life' so to speak: shops, restaurants, main squares, monuments, etc. So while yes, if you ask about the centre everybody will point Plaça Catalunya, note it's not "required" to stay there (more expensive and more crowded!) to live up the city.

Thank you for your thoughtful reply. I completely understand what you mean when you say that Barcelona has no real town center. Perhaps that is why so many people recommend different areas to stay, because different neighborhoods appeal to different personalities and they are all a "center" in their own right. That being said, I am leaning towards the apartment on the El Born/Gotic border. I think the charm of the neighborhood is worth putting up with some tourists and their rowdiness.

"...are protesting about the use of apartments illegally for vacation rentals."

I'm afraid that's not so... the problem is not the use of illegal apartments per se, the main problem is focused in the sort of unruly disrespectful tourists that have in recent years flooded the area -and some others in town. Pretty much every Barcelonian -me included- from that and other districts support the claims of the neighbours of La Barceloneta because we all have seen the problems at one time or another. Barcelona is, and has always been, a welcoming city open to visitors, immigrants and expats -in fact, 18% of the city 2 million inhabitants are of foreign origin and the city hosts 8 millions visitors every year. The problem comes when a reduced group of those visitors think anything goes here, puke and piss on the streets, party all day and night long without respecting neighbours, vandalises public furniture and cause trouble. Some visitors have clearly mistaken our welcoming easy going Mediterranean character with a totally unacceptable attitude. That's the real problem. In any case, note that Barcelonians are very protective of their city so, mark my words, this will certainly not turn into some of those 'wild crazy destinations' we all have in mind -rather not to mention! Wait and see.