The city of Aspendos, commonly believed to have been settled by colonists from Argos, lies a few miles beyond Perge on the Antalya-Alanya highway. I suggest that you tackle both as a pair.
There's not much left of the ancient city, but the one remaining monument, the Theatre of Aspendos, is enough to warrant a trip. Thanks to the high-quality calcareous stone and the fact that the Selçuks reinforced the structure during its run as a caravansaray, this 2,000-year-old theater is the best-preserved ancient theater in Asia Minor and the best example of a Roman theater in all of Pamphylia. The best way to visit the theater is to see it as it was meant to be, during the national opera and ballet festival in the summer, but it's an awesome sight without the show.