I'm with sassafrass in that I wouldn't penny pinch. My personal choice would be to give up some travel time so that I could afford to actually take advantage of the unique opportunities that any place I do visit affords. JMO, and of course, viva la difference!

Unfortunately, I found each of these places worthy of a visit and refuse to try to put them in any kind of rank order. Again, JMO.

I agree with kja!

If you just see the Sagrada Familia from the outside, you're missing a lot. The stained glass windows are not like the medieval ones; they're huge and cast a stunning light over a wide area of the interior. Google Images of the church to get an faint idea of the experience.

And do buy tickets ahead of your visit. The lines can be long otherwise.

Full disclosure: I'm not a big Gaudi fan. I'm an engineer and all those curves seem goofy and hard to build.

Even so, the Familia Sagrada was very impressive. It's a "can't miss" if you're in Barcelona. But be prepared. The crowds can be overwhelming; we were there a year ago in mid September and it was a crush even then. Also, as noted above, there's ongoing construction that detracts from the building. But it will be that way for a few years so there's nothing you can do.

We passed by the two houses and enjoyed them from the outside. Didn't feel the need to go in. Seemed expensive. And we skipped the park. With only three days in the city there were other things we wanted to do more.

You didn't ask but here's a personal note on the Picasso museum: Most of the paintings were from one period (maybe the early 1950's?) and not representative of Picasso's work generally. With your limited time I'd skip this one. We were disappointed.

As an engineer, you were probably impressed with the column design--I know I was even though I'm not an engineer.

I agree with kja. You really should see more than one Gaudi site. We visted Sagrada Familia, Casa Battlo, Casa Mila, and Parc Guell, and loved all of them. They are each very different from the other. We preferred Casa Battlo over Casa Mila, however.

Not sure what lines will be like in May. We were in Barcelona in October and the lines were not awful. Just be sure to get there before they open, especially Sagrada Familia.

@Ackislander - thanks for the reply, but I am no wiser, or at least not convinced. I am a huge Art Nouveau fan. If I am paying a high price to visit a Modernisme building, I expect to see a Modernisme apartment. I found the contrast totally without interest and felt conned.