Several tea rooms operate within the walled town, serving the steady flow of visitors who need refreshment after the castle or the wall walk. The best of them are straightforward: decent tea, Welsh cakes, bara brith (a spiced fruit bread that is the unofficial national cake of Wales), and sandwiches. Nothing fancy, but exactly what the situation requires.
Look for places on or just off Castle Street and High Street rather than on the tourist-facing quayside, where prices tend to be higher and quality variable. A warm slice of bara brith with butter is one of the more honest pleasures Conwy offers.