Barcelona is one of the most interesting and beautiful cities I traveled to. The artwork/architecture of Antonio Gaudi gives the city a cartoonish feel with La Segrada Familia and Park Guell. I stayed at Habana Home Hostel Hostel (Escuedeller, 20 Principal) off of Las Ramblas which was really confusing. Trying to find a side street off of Las Ramblas is not the easiest thing to do. Just a little story to go along with my trip: Me and a friend stayed at a hostel with blackout curtains because the Spanish like to sleep in...and go to bed mid morning, unlike everyone else in the world. Well we went to sleep alright, but were awakened with a gentleman who had night tremors and was yelling at the top of his lungs and kicking the bed my friend was sleeping on. This was freaky at the time, but a great story now, hostels are always interesting.
Another good way to see any city is to use the hop on hop off bus tours. I know this seems like a cop out but for those of you on a budget and that dont speak the local language, it's a good way to get a cheap ride to the best sites and hear a little history along the way. If you are backpacking and don't plan too much in advance for siteseeing, its the perfect compromise. (Alot better than paying a taxi that can lead you around and charge extra)