Before I went to Barcelona in 2004, I asked a friend who had lived there what are the must-sees. He said, "Everything Gaudi." I must confess, I had no idea who or what Gaudi was. When I found out that it's all about architecture, I basically lost interest.
I arrived Barcelona at night and met up with a friend of mine. The first words out of her mouth were, "I LOVE Barcelona." She took me to Casa Batllo, one of Gaudi's masterpiece. It took my breath away. I had never seen, nor could I, imagine something like that. I fell in love with Gaudi's work immediately.
Although La Padrera is not my favorite, you should start your Gaudi exploration there. It has a small museum area that has various model designs. It gives the visitor a great intro. Then I would go back to Casa Batllo. The audio tape is mandatory for entrance. But don't let that turn you off. It is well worth it. Another must-see for Barcelona is Gaudi's unfinished masterpiece is Sagrada Familia. You can't miss this one with it's tall spires. Again, the audio tour is worth every penny. Don't get skimpy here.
Lastly, a lot of visitors miss Park Guell. It's a little inconvenient to get to, although not very far. You have to walk for about 15 minutes. I went in mid-day. If you could go at sundown or dusk, I think it would make the visit even more beautiful. The entrance to Park Guell is free. Inside there is a museum that charges an entrance fee. If I were you, I'd skip it. It was not worth the money. Save your money for a glass of Sangria to top off the day.