Barcelona is one of my favorite cities - one must walk Las Ramblas - and the Gothic Quarter and visit Mercat de la Boqueria (neat counter-style eateries there using all fresh seafoods and local goods) - I enjoyed eating at Les Quatres Gats in the Gothic Quarter (just don't sit in front of the piano!) one of Picasso's old haunts -
I really liked walking through Park Guell (Gaudi's park - easy bus ride up the hill from The Triangle) - a little hike up to the cross at the top of the path, you can see all of Barcelona and beyond. I enjoyed the Casa Batlló (Gaudi design) more than I did Sagrada de Familia.
Last summer, I visited El Born and the church of Santa Maria del Mar - first time in that area. Brilliant! The stones of the church were carried on the backs of the working men - it was built as a church for 'the people.' Immediately came home and read Ildefonso Falcones's Cathedral of the Sea
Another treat was eating at Cuines Santa-Caterina restaurant and tapas at the Santa-Caterina Merkat - I was with friends from Lleida and would never have found it otherwise. A treat!
I love Barcelona....
If you would really like to have a tour guide recommended, pm me - some in my party found an excellent guide.