On Avenue de La Reina Cristina, an unpromising but quite central street full of electrical shops, there is Can paixano - a tapas joint and cava wholesaler.
Glass of cava from 1euro, buy a couple and you'll get a free snack. Or buy some food and then they let you buy a bottle of cava (Very decent stuff about 6 euros, cheaper available).
Tends to be standing room only, but there is nowhere else you can stuff your face with delicious food and get shitfaced on fizz for so little.
Have a look at runner bean tours. They are free walking tours and very good. Also try the Paella at Meson Jesus in the back streets behind Las Ramblas. Get a T10 metro ticket. 10 trips for 10 euros 80cents