I’d highly recommend Jesus’ place. The position is perfect close to the market, in the centre of the old quarter. It is close to La Palau de la Música the Cathedral, the Picasso Museum and Museum of Modern Art. The hop on hop off bus is a 2 minute walk from his place.
Jesus is a very thoughtful host and is available to help via text if you get lost or can’t remember a place he suggested. I felt very safe at his place and it wasn’t noisy late at night.