The village halfway along the gorge is the obvious lunch stop. A handful of riverside restaurants set out cushions and low tables on platforms in or over the Melendiz, and you can take your shoes off and eat trout with your feet in the water.
Nothing is fancy and prices are reasonable for what they are. Grilled trout, gözleme (stuffed flatbread cooked on a saç), and tea are the standard. If you want to break the walk and continue in the afternoon, this is the place to do it.