Perhaps less well known than Catalan artists like Dalí and Miró, Antoni Tàpies was a delightfully strange painter, sculptor and art theorist, and Barcelona's museum dedicated to his work is located just off Passeig de Gracia, making it much more easily accessed than Fundació Miró on Montjuic. To me, at least, his early work resembles spookier, artsier version of gothic comics, and later paintings and sculptures are objects as art on par with Marcel Duchamp's fountain sculpture made from an upside down toilet. Some of my favorites at the museum include a chair piled with clothes, and an open wardrobe nearly exploding with garments.
The museum is also worth a visit to get a look at temporary exhibitions, or check out its outstanding art and architecture library (only with prior appointment). The gift shop has a few interesting Barcelona art souvenirs and neat postcard sets.