There is one small café at the entrance to the archaeological site, another at the Troy Museum, and a couple of village restaurants in nearby Tevfikiye. None are special. Most visitors eat in Çanakkale before or after, where the seafront restaurants serve excellent fresh Aegean fish — sea bass, bream, calamari — with the standard Turkish mezze. The town's grilled meatball restaurants (köftecis) along the central market are cheap, fast, and good.
If you are at Troy for a full day, bring water and a snack. The mound is exposed and the walk back to the café is a long one in summer heat.