First of all, Alejandro and Fernando are great hosts: both speak good English, very easy to reach via mobile or airbnb and very very helpful with everything.
Here are my points (we stayed 5 days, 3 people):
1. it's very easy to get to the apartment from the airport: buses run every 5 min and bus stop is only 100 meters away from it.
2. 10 min walking distance to the centre of Barcelona.
3. Apartment itself looks exactly as on the pictures. Clean, cozy, stylish and all you need is there. Due to weather we couldn't enjoy the balcony, but that would be cherry on this cake.
4. Very quiet, no street noise at all! Yes, you can hear the elevator, but that is really nothing, especially if you compare it to the noise of the streets of Barcelona.
5. Two supermarkets are around the corner, restaurants are also near by.
Highly recommended. :)