First time to Dalyan - then you have a great treat awaiting you!! As the others have said, there are cafes at both ends of the beach. At the boat end, there are ladies who sit and make those delicious gozlem (pancakes) with either savoury - cheese or meat, or sweet - honey and banana, hazelnut cream.... fillings. Some years there also was a man who would fry meat to put in fresh bread. The cafe itself will make you up a toasted sandwich or toast, and also serve all sorts of gateaux type cakes, along with tea and coffee, soft drinks, water or cold beers. Also icecreams, and fresh fruit.
The cafe at the other end is smaller since fewer people go that end, but again do the full range of beverages and sandwiches etc - but not the gozlem or kebabs - or at least they didn't last time I was there.