Thanks for the info update :)
Late May is a bit of a tricky time to visit the countryside, as it's on the tail end of the rainy season in the North but at the beginning of the Summer heat in the South (i.e. Andalucia), granted it's not as hot as in the high summer months. I'd say in general you are fine to visit Andalucia, but you may still need to take into account the potential for heat, as it's a bit unpredictable.
As others have posted above, the White Hill Towns of Andalucia are the most popular choice, albeit quite "on-the-beaten-path", it's certainly not undiscovered, if you get my drift ;-) You can fly in to Sevilla, rent a car there and then head up to Arcos or Ronda which make for fine bases, with Zahara and Setenil making for smaller more intimate experiences.
On the other hand, allow me to suggest a few alternatives, which are no less spectacular and charming, yet are off the radar, as far as international tourists are concerned:
Extremadura: Fly in to Madrid and rent a car then drive southwest through the Extremadura region, a land of time warped Crusader Castles, Moorish Strongholds, Royal Monasteries, and impressive Roman ruins: stopping in places like Cáceres, Trujillo, Guadalupe Monastery, Mérida, Zafra. This is the region which the Holy Roman Emperor Charles the V retired to, it's also home to the best quality of Jamon Iberico in Spain.
Southern Aragon: Fly in to Valencia or Zaragoza, rent a car and then drive to this undiscovered corner of Spain. Center yourselves around Teruel, known for its Gothic and Islamic architecture, and then branch out to Albarracín (voted the prettiest village in Spain) and to ancient Calaceite. Also make a side trip to nearby Matarraña, nicknamed the "Tuscany of Spain".
Hope this gives you a few ideas :)