One of the best bars in Barcelona to meet people is L'Ovella Negra - the Black Sheep. This bar is located just off the top end of Las Ramblas near Boadas Bar on Carrer Sitges, which is a little alleyway, typical of Barcelona's Old Town.
The reason why it's such a great place to meet people is because of the size. Most of the bars in the old town are small and narrow, but - depsite the appearance from the door outside (you almost have to stoop to get in) - The Black Sheep is big. The website calls it a Tavern, and I suppose you could say that's right, with the old stone walls and huge trestle tables and benches. The waiters will only serve you at a table (or a barrel) and serve big jugs of beer or Sangria. You can also get spirits at other drinks at the bar but mostly the big jugs go down well. It's inevitable that you sit down next to a group of people, or newcomers will ask if they can squeeze on your table, so exchanging stories and meeting both locals and international travellers is really easy! There's a table football area towards the front and a pool table in front of the bar, too. Many of my best nights out when I first arrived here started at the Black Sheep. Check it out.
For your accommodation needs in the city, try apartments for rent in Barcelona as a great alternative to hotels. And for more city information, check out this great Barcelona Guide.