One of the things my kids liked to do was pretty easy....simply walking into the Mediterranean! There is a lovely sand beach and you can walk right into the water, reveling in the fact that you are in the Mighty Mediterranean (for us it was very exciting). We went in April and even then the water was pretty warm and it was very exciting to be in the great Sea, especially if your daughter has had any exposure to the Med. through her social studies class.
Our kids loved the Gaudi house, Casa Batllo. It was much less expensive and more manageable than Sagrada Familia. It has a audio guide that our kids enjoyed listening to and gave them some freedom to walk around on their own (this was a false freedom as they had to stay within our sight, but they seemed to like the independence). They liked the crazy colors and the wavy walls.[Casa Batlo: http://www.tripadvisor.com/Attraction_Review-g187497-d191052-Reviews-Casa_Batllo-Barcelona_Catalonia.html.
We also liked Parc Montjuic, a large fortress overlooking the Mediterranean. It is in the city and easy to get to but is a bit apart, it is enormous and very spacious and my kids liked being outdoors with some room around them (unlike other areas of the city). Plus to get there we took a cable car with stupendous views! I'm going to try to put in some links from Trip Advisor but not sure they will work---my apologies if not: enter link description herehttp://www.tripadvisor.com/Attraction_Review-g187497-d2359212-Reviews-Parc_de_Montjuic-Barcelona_Catalonia.html
We also liked Placa Espanya, which was near the area of Montjuic. Again, http://www.tripadvisor.com/Attraction_Review-g187497-d591343-Reviews-Placa_Espanya-Barcelona_Catalonia.html
Lastly, the kids did like Parc Guell, but I understand there is now a charge to enter, and I understand it can be horribly, horribly crowded (wall to wall people) which would detract from the experience. You might be able to do some research to investigate when the least crowded times are. It has wonderful Gaudi mosaics and statues, I would try to see it if I could get a hint as to the best times to go.
Lastly, Las Ramblas is a famous sidewalk with lots of vendors/booths alongside the walkway. Lots to look at...vendors that sell parrots, rabbits, fruit/vegetables, bread, seafood, as well as junky souveniers. There were a number of street entertainers, people who were "live statues" etc. This is not something my kids see frequently so they were mesmerized. But this is PICK POCKET ZONE so be very very careful.
Enjoy! Private message me if you have other questions.