Also known as The City of Gaudi, it's only fair to say:
Barcelona has some impressive architectural sights. The capital of Catalunya is getting more popular among tourists each year, mostly because everywhere you look, you can get a taste of the unique Catalan Modernism, an important characteristic of the province. If you have never been here before, it's a good idea to start your tour with the major attractions.
For starters, go see the never-ending master-piece, the Sagrada Familia. And in order to get a more accurate understanding of why art isn't to be rushed, go see other important (but finished) creations like the facade of Casa Batlló, the apartment building La Pedrera and Park Güell.
After so much wandering around, you deserve a break by La Rambla, the famous thoroughfare. If you walk down the street, you arrive at Mirador de Colom (with the Columbus Monument). While sightseeing Rambla de Mar and the bay, you can visit the the most important Mediterranean science centre in the world, the aquarium (L’Aquàrium de Barcelona).
By the end of the day, you can relax watching and listening to the impressive water and lights show of Font Màgica on the Montjuïc Castle hill. If you are in The City of Counts for more than 3 days, make sure you find a way to get to the Montserrat Monastery and/or Figueres (the birthplace of Salvador Dali and the most amazing Teatre-Museu Dali).
Personal Recommendation: Have brunch at el Petit Princep