Ufff! I have a little bit more time today to write about this subject. I had to write my earlier post very quickly because I was heading to....you guessed it, Zaragoza for the Easter break.
Apart from 'La Basílica del Pilar', which is essential, the Virgin of El Pilar (the pillar) is the Patron Saint of all the 'Hispanidad' (Hispanic world, I guess you could call it); you must visit the nearby 'La Seo', and the moorish 'Aljafería'.

Besides that, I can think of a must-not-miss place, if you're into delicious ice-cream, try the Helados Italianos chain (several locations); they're 100% natural and gooood!, and I'm not saying this only because their tutti-frutti flavored one was one of the best things about my childhood! :p
If you're not "veggies" (and by that I mean 'vegetarianos'), you should eat, while there and at least once, 'ternasco de Aragón' (Aragón being the region where Zaragoza is located). Right Shawn? .Also, there is a typical vegetable there called 'borrajas', I personally find them delicious, it's too bad it's extremely hard find here in Madrid (apart from El Corte Inglés ), and when you do, it's pricey and not good quality.

I'm not so sure you'd have to pack up a lot of heavy clothes if you headed up for Jaca, for example, in the 'Pirineos'; rather some heavy blankets in your beds at night.

Enjoy!!!

P.S.: Do buy some 'longaniza' there too, I can't say "bring home some...." because it's a pork product, so I seriously doubt that you could. I'm glad I have,....I'm savouring it as I write!