This apartment looks to be the best place to stay on the block. It's the only (or one of the only) places with a lovely terrace, which we enjoyed before and after we went out to explore the city. The space is very clean and everything worked smoothly. Even though it's not super close to some of the tourist attractions (La Sagrada Familia, Parque Güell, the beach), we still enjoyed walking to the beach and dinner and decided to take a cab to see Gaudí stuff (metro workers were on strike). We only had one full day to explore, but were able to fit everything we wanted in. Maria Luisa also left us some champagne and fresh oranges, which was very lovely (and delicious!).
One thing I'm not sure of is a small charge we were asked to pay when we got there. Not being familiar with AirBnb rules (this was our first time), and the charge being so small (about 5 euro), we didn't argue, but looking back I don't see any mention of it in the listing.
Also, be aware that Spain requires the host to send passport info to the police for your stay.
Overall, we very much enjoyed our time in Barcelona and this was a perfect place for our short stay!