Baeza is a small town of about 16,000 in the Andalusian province of Jaén. It's a bit off the beaten path for most tourists, though as home to some of the best-preserved examples of Italian Renaissance architecture outside of Italy, it is well deserving of a detour.
The town is small and sleepy and feels a bit stuck in the past, but the people are as friendly as can be, the buildings are beautiful, and the tapas are free. It's a small enough place that you can wander it in a day and pretty much see all there is to see, but be sure to stick around long enough to grab some cañas and tapas at one of the neighborhood bars and take in an underground (literally) flamenco show at the local Peña de Flamenco. There's nowhere better to immerse yourself in an authentic Andaluz experience.