Almost everyone makes the same mistake at the Met: they stay too long, come out starving at 2:30pm, and eat whatever is directly in front of them on Fifth Avenue. Fifth is the worst block for food in the entire neighborhood. It's museums and apartment buildings and one hot dog cart. Walk one avenue east to Madison and the whole thing opens up.
Here's the shape of it. The Met sits at Fifth Avenue and 82nd Street. Everything worth eating is either inside the building, four blocks north at the Neue Galerie, or on Madison between 75th and 86th. Nothing on this list is more than about eight minutes on foot from the steps.
We're at 341 East 62nd Street, so we do this walk often. From our door it's roughly 25 minutes straight up Fifth with the park on your left, or you take the Madison Avenue bus and let it drop you at 81st. The bus is genuinely the smart move in rain or in August. The other option, and the one we usually pick, is to walk up through Central Park from the Fifth Avenue entrance at 60th and come out at the back of the museum, which turns the trip into a proper walk instead of an errand.
A few timing notes that make the difference between a good lunch and a bad one. The museum's own cafes are at their worst between 12:30 and 2pm, when every school group in the tri-state area is queuing. If you're inside during that window and you're hungry, either eat early at 11:45 or push through to 2:30. If you're planning a real sit-down lunch, book it. The Madison Avenue rooms up here are small, and on a Saturday in October they fill with people who live four blocks away and reserved on Tuesday.
And if you're doing the Met as part of a full Museum Mile day, eat between museums rather than after. The stretch from the Met at 82nd to the Guggenheim at 89th is short, and Cafe Sabarsky sits almost exactly in the middle of it. That's not an accident of geography we invented; it's just how the mile is laid out.