Raval still has its share of remarkably pretty areas, such as around Doctor Dou, Pintor Fortuny and just south of Macba. Those in-the-know will take an apartment in Raval for its cool bars (try Flamingo or Manolo), cheap supermarkets and grocery stores, basically more dash for your cash, eg vacation apartment with huge sunny roof terrace for evening (or morning) drinks:
www.waytostay.com/Barcelona-apartments-en-52-2503.htm
35 euro per night each with a location just off La Ramblas is about as good as it gets in Barcelona.