While visiting Barcelona, do yourself a favor and take the roughly two hour train trip from Barcelona to Figueres. The highlight of this daytrip is most definitely the Teatre-Museu Dalí (a well-marked fifteen minute walk from the station); the small town is most famous for being Salvador Dalí's birthplace and home to the museum he built. The museum is a worthy monument to a great artist and his longtime wife, companion and muse, Gala.
The Museum sits on the site of the former municipal theatre (destroyed during the Spanish Civil War) and was designed by Dalí himself. It is also where Dalí is entombed (though you need to have a keen eye to find his actual gravesite). The Gala-Dalí Foundation manages more than 4,000 of Dalí's works- including paintings, sculptures, jewelry, engravings, photos and holograms. Much of the work is on permanent display at the museum while other parts of the collection appear in temporary exhibitions in the museum and abroad. The architecture of the museum is made specifically by Dalí for his life work and, in fact, the design could be considered his crowning achievement.
Every visitor has their own "must see" list, varying from the car that you can water, the room that, when viewed from above, looks like Mae West, and the multitude of recognizable famous pieces. No one leaves the museum unimpressed. The cost of admission is 10 € (which includes admission to the Jewelry Exhibit) and the museum is open Oct.-June, Tues.-Sun. 10:30-5:15; July-Sept., daily 9-7:15.
If you want to explore the area further and you are a huge fan of Dalí, you should also consider checking out the House-Museum Gala Dalí Castle in Pubol (where Gala is buried) and the House-Museum Salvador Dalí in Portlligat.

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