RS does not specify reasonably priced places to eat in Eze. I would welcome suggestions for $-$$ cafes/restaurants for dinner and perhaps a place to get sandwiches for lunch. We will be hiking (in decent but practical clothes) through the village, so a relaxed vibe is desired.
Might try posting your question in the Q&A section under France. This section is for reviews after you have visited the restaurant.
Eze village is pretty small. Except for the restaurant at the hotel at the top, I’ve never seen any recommendations. Maybe someone on the Trip Advisor forum would know.
Le Nid d'Aigle. https://www.leniddaigle-eze.fr/ But remember: you will eat what is on the menu, no changes possible.