I think MacDonalds still does free wi-fi across Europe. Starbucks used to but now you have to have a rewards card to get it - like a gift card but you get bonuses.
Had a nosey on this site:
http://www.wififreespot.com/europe.html
Barcelona
Bar Daguiri - Grau i Torras 59 - Barceloneta Beach C/Veguer 13 - (Pl. del Rei) - +34933100435
Biblioteca Museu Maratim - Av. Drassanes, s/n Cat Bar - Boria 17
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Hotel Apsis Atrium Palace - full hotel coverage - Gran Via de les Corts Catalanes, 656
Hotel Apsis Millenni - full hotel coverage - Ronda Sant pau, 14
Hotel Regina - Free wifi wireless coverage in the lobby and common areas. - Vergara street 2 & 4
Hotel Condes de Barcelona - full hotel coverage - Passeig de Gr�cia, 73-75 Hotel Apsis Aranea - Free wifi wireless coverage in the lobby and common areas - Consell de Cent, 444 - (+34) 93 247 74 74
Hotel Lleo - full hotel coverage - Carrer de Pelai, 22-24 - (34) 93-318-1312
Hotel Colon - Free wifi wireless coverage in the lobby and common areas - Avenida de la Catedral, 7 - 34-93-301-14-04
Hotel Mariano Cubi - C/ Mariano Cubi, 62-64
Hotel Praktik Rambla - Rambla de Catalunya 27 - 933436690
Hesperia Carlit - C/. Diputaci�n, 383
Hesperia Del Mar - Espronceda, 6
Hesperia del Port - Avenida Paralelo, n� 40
Hesperia Metropol - Ample 31
Hesperia Presidente - Av. Diagonal, 570
Hesperia Sarria - Los Vergos 20
Hesperia Castelldefels - Paseo Maritimo 138
Hesperia Sant Joan Suites - Josep Trueta 2
Hesperia Sant Just - Frederic Mompou 1
Yellow Nest Hostel - pasaje regente mendieta - 934490596