One of your first stops should be Centro de Interpretación de Adamuz. Here, you'll be able to orient yourself and get lots of useful information before you set out exploring.
You'll be spoiled for sightseeing choice when spending time in Adamuz. Centro de Interpretación de Adamuz is a good place to start here, but there are lots of other fine places to explore. Aquasierra, Tower of Garci Mendez, and Centro del Olivar de Sierra-Adamuz are near the tourist information center and will fill in your day nicely.