For a change in scenery, and beaches that you will be the only human being for kilometres, head west to Cilician Mountains.
You will certanly start to feel Middle-Eastern influences in culture, cuisine, and architecture while in Cilician Plains; for a lot more, head south to Hatay, from where trips further on to Syria can be arranged easily keep the visa issues in mind, though.
Southeastern Anatolia to east is another destination with much Middle-Eastern influences, and with impressive ancient towns.
Just north of the mighty Taurus Mountains, across the Gülek Pass known by Cilician Gates in ancient times, Cappadocia awaits.