Staying at José's is definitely a great choice.
I've spent in Barcelona only 2 nights and the position of the apartment made it super easy to get anywhere: anything located in the city center is at a walkable distance from the house, and anything else is easily reachable with all the bus lines and subway stops nearby (airport included).
Yet, the bulding is located in a very quiet area, which is something very rare in Barcelona, where usually you have to choose between being in the center or being able to sleep.
I didn't have the chance to enjoy the apartment much since I was always out, but it has some great areas to relax and it's kept squeaky clean.
José is an amazing host: very attentive, helpful, precise and replies very fast to any question you might have. My flight landed with more than 1 hour of delay and he was very understanding.
I would definitely recommend it to anybody staying in the city :)