I eat lunch here pretty much every time I stop by the art museum and the food is great, actually excellent. I've been around to many museums and none of them have food like the Cleveland Art Museum.
I've had their pizza, grilled lamb on pita, salads and I can't think of anything bad to say. The one item that I didn't think looked great was their noodle salad! They also serve beer and wine if that is of interest to you.
Seating is usually packed in the cafe, but you can also sit outside in the atrium. Even if you are not going to the art museum this is a great place to stop by for lunch since admission is free.
Expect to pay $10+ by the time you get a drink... Members of the museum get a 10% discount.