In another post we said that the Raval is the poorest neighborhood in Barcelona, but there is an area that has been changing for years and now is full of bars, shops and fashion places.
Look for the MACBA (Plaça dels Àngels 1), the modern art museum in Barcelona. The building is nice, although it is always full of people jumping on skateboards.
We like the CCCB more (Montalegre 5), where there is always some interesting exhibition. Behind you can have a drink in the Plaça Joan Coromines, which is usually very quiet.
Right next to it there is the Pati Manning (Montalegre 7), a very nice building where there is a restaurant.
But the best part of the neighborhood is walking through its streets. Go to streets like Joaquim Costa, Elisabets, Doctor Dou (very nice shops) or Ferlandina, where you can buy some good empanadas in Muns (Ferlandina 37).