If she's an art student you have picked a brilliant city. You need to do Parc Guell and the Gaudi houses as a must. Can you hire a car? If you are in Catalonia it would be a shame not to take in the Dali museum in Figueres, its about an hour and a half away and well worth the trip. The jewellery display is amazing. Sagrada Famillia is amazing too and well worth the entry fee.
I would get off the Ramblas to eat as if you go up the side streets its better food for half the price. I would go to La Boqueria (sp?) market on the Ramblas too and stock up on goodies for a beach picnic.
The only thing in Barcelona that features on the tourist guides which I find overwhelming is Montjuic, I think you need to really love sport to get anything out of it.
If the weather is nice, it's also great to wonder down to the beach, and visit one of the beachside cafes, or at the Marina. The tapas is quite reasonable in price and the fish is usually fresh and tasty.