Bermejas Towers, Granada
You can find these very old towers as you enter the Alhambra park at the top of Calle Gomerez off of Plaza Nueva. As you enter the park take the path to the far right.
Once you get there don't just walk back down again; if you keep walking up you will find there is a lot more to see in the area apart from the Alhambra!
Some say the towers might be older than the Alhambra.