Here are a few ideas:
First, following up on the architecture thread. Although Gaudi is the best-known (and most flamboyant) of the Catalan "moderists," he's not the only! His contemporary and sometime mentor, Lluis Domenech i Montaner, deserves some attention, too. Barcelona has two of his best works. The old Sant Pau hospital campus, which is just a few blocks of the pedestrianzed Avinguda Gaudi from Sagrada Familia. It's presently used as a cultural center, and consists of a series of buildings with a common theme but great variation, linked underground by utilities. His other Barcelona masterpiece is the Palau de Musica Catalana, which is not only gorgeous but admired for its acoustics.
Second, if your friend has any interest in science, the Cosmo Caixa, partway up Tibidado, is one of the world's best and most absorbing science and technology museums. Its exhibits are incredibly varied, many are interactive and watching familes with children enjoy the museum is almost as good as the museum itself.
Third, if the aquatic exhibit in the basement of Cosmo Caixa isn't enough fish for you, the Aquarium on a pier at Barceloneta is also world-class. And within easy walking distance of edible fish and seafood at numbers of cafes and restaurants on the beach side of the Barceloneta boardwalk.
Also not far from Barceloneta is the Museum of the History of Catalonia, which traces the history of Catalonia and Barcelona from ancient times to present day; while it has an admittedly Catalan nationalist bent, it's also one of the few museums in Spain that takes a clear look at the Franco era.
A day trip to Girona, north of Barcelona, makes a nice day. It's an old university city, with a sizable medieval core and modern development; the old city wall has a walkway along a large part of it, giving interesting views of the old city and of parts of the newer area.
There's a cable car from near Barceloneta that runs up to a high point on Montjuic; the views are spectacular, and when you get off, you're not far from the MNAC, the national art museum of Catalonia, where you can see what 19th-century Spanish and Catalan painters were doing while their more famous French Impressionist contemporaries were working, as well as a large collection of older masters.
Somewhere else on these forums I said that Barcelona can absorb as much time as you give it, and it's true...but tell your friend to save some of it for himself...to sit in the park, to hang out at a cafe, to go to the beach!
The best part of every trip is realizing that it has upset your expectation!