I wouldn't stay on La Ramblas, it's like O'Connell Street, nothing special and a bit rough. There are lovely pedestrianised places within a short walk of La Ramblas that are much nicer. Depends on what you want.
I booked a studio apartment in El Born beside Santa Maria Del Mar. It's a lovely gothic area with nice restaurants, pubs, shops, street entertainers and cafe scene at night time. La Ramblas and the Marina are within a short walk (maybe 10 mins).
Actually this is the exact apt I rented and the site I booked through:
[broken link removed]
The apartment is up a narrow alleyway but once you've found the church Santa Maria Del Mar you're beside it. I'd go for any apt around this area.