Buy a T10 Metro ticket on arrival. This gives you cheap travel on the Metro. Of course, La Rambla (or Las Ramblas) must not be missed. Visit the port area and the old quarter. The open top bus tours (night and day - 2 day ticket recommended). If you dont visit Sagrada Familia, you might as well stay at home.
Soak in the Barcelona atmosphere. Look at the architecture, the design of streets and street intersections, the shopping, the light, the restaurants. The restaurants get cheaper the further you get from La Rambla and Sagrada Familia. But, you're in Barcelona pay the few bob extra.
Pickpockets:- Yes, Barcelona has more than its fair share of pickpockets. Most people deserve their pickpocket fate with bulging wallets sticking out of the back pocket of jeans (manna from Heaven for Fingers Gonzales). Place some beer mats in a cheap wallet "bulging from your back pocket" and let Fingers enjoy Cerveza Sol adverts.
Dont fall for a jubiliant Barca Fan throwing his arms around you singing "Amigos par siempre" while simultaneously relieving you of your wallet either. Lift you knee as fast as you can and enjoy your new 'amigo' rolling on the ground in front of you.