I stayed about a month in Mabels apartment and can totally recommend it. It is located right in the center of the old city and within a few steps you can reach Rambla del Born or Carrer de Princesa where many bars, bakeries, cafe, etc. are located. In about 15-20 minutes you are at the beach (Barceloneta) or Plaça Catalunya which is a major public transport hub of the city.
The apartment is on the fourth floor. As indicated there's no elevator and the stair case is really tight but it is totally worth it climbing up.
The kitchen etc. is super equipped and I did't miss anything. Mabel is very welcoming and was always helpful, friendly and supportive. Again - I can recommend it .