For someone who is more interested in history or nature, but not so much museums, here would be some of my recommendations for day trips around Madrid and Barcelona.
Near Madrid:
Toledo - a stay for a night or two in this medieval town will feel like living in history, especially at night.
Roman town of Segobriga - an intact Roman town that was completely abandoned during the very early middle ages, only recently begun excavations, relatively undiscovered by most foreign and even local tourists.
Cuneca - 12th century medieval town built on the steep side of a mountain, which makes for a very unique place to spend a day or two.
La Ciudad Encantada - close by to Cuenca, one finds a protected geological site with many large and unusual mushroom rock formations, many films were shot here, including Conan the Barbarian.
Near Barcelona:
Tarragona - has some of the better Roman ruins in Spain, including a Roman amphitheater and Praetorium tower. The medieval center also makes for a nice place for walks and dining.
Pont del Diable - close to Tarragona, there is an intact Roman Aqueduct. You can actually walk over it like a bridge (if you dare). The surrounding forested area is great for some casual hiking too.
Girona - ancient city in northern Catalonia, it has an impressive Cathedral, towering medieval walls, and narrow winding streets, The Onyar river snakes it's way through Girona, giving the town a Florence-esque feel
Empúries - the site of the ancient ruins of a Greek colony from the 6th–3rd century BC. It's quite unique as the ruins sit right on the Costa Brava overlooking the sea.
Hope this gives a few ideas! :)
