I have stayed in this area three times recently, and I think it is the best place to stay in Barcelona. In the second picture you can see the place we rented on the last visit on the left. Right next to the Cathedral, and near some other major sites, it was a pretty amazing experience.
The area is far from perfect; Barcelona is a big, butch city, and all the nightclubs etc. in the old quarter mean there’re lots of very young people making a big, smelly mess.
However, this is a huge, American-style grid city, and this is a different, more European part of town with an old atmosphere. The history here is incredible, and – once you figure out the crazy-winding streets – it is a fascinating location for a visit.