Go to the Picasso Museum for art. There is also a beautiful Modern Art Museum. (can't remember the name) I would also make sure to see Sagrada Familia and Parc Guell, which was designed by Gaudi. There is also Guell Palace that is spectacular to see. (Guell was Gaudi's patron so you see Guell all over Barcelona) I would hit the Boqueria for a breakfast at one of the counters. I loved seeing the fortress at the top of Monjuic and the Olympic Stadium. There is lots of other stuff to do but for 36 hours, you can only hit the highlights.
There are great restaurants too. Stay away from the ones on Las Ramblas, tourist traps and not very good.
I love Barcelona.