None of the cafes or restaurants along the Corinth Canal out of town or along the waterfront in town deserves to be singled out; most deserve to be avoided. Similarly, the restaurants near the ancient site tend to have high prices and mediocre food. That said, following are a couple suggestions if you find yourself hungry in Old Corinth (and can't wait until you get to Nafplion, which has a number of good places to eat).
Locals speak well of the grandly named Splendid restaurant across from the site; a lunch or dinner of simple stews, chops, and salads costs around 15€ ($20). The Ancient Corinth on the main square offers much the same food at similar prices.