My favorite part of visiting Barcelona was exploring the small winding streets of the Gothic Quarter, also known as the "Barri Gotic". This is the oldest part of the city and it is a veritable maze beautiful, picturesque buildings dotted with little shops. I really could have spent our whole time in Barcelona just wandering those little streets. As you wander along there are numerous bakeries and little sandwich shops where you can stop to get a bite.
Mostly you only saw pedestrians on them but every once in a while a car would squeeze its way through. And I did see the classic sight of a Barcelona resident on their bicycle with a large baguette strapped to the back.
Tucked among the winding streets is the Picasso museum. I have no pictures from that because you can't take pictures inside and the outside looks like nothing -- just another entrance with a tiny sign. It was difficult to find but really worth!