The grid does strange things where the avenues cut across it on the diagonal, and the Flatiron is the proof: a building shaped like the slice of land it sits on, six feet wide at the prow, jammed into the wedge where Broadway crosses Fifth. This walk is a chain of squares strung down the grid from there to Union Square — public, private, and the one you can only look at.
Start at the Flatiron's point, then cross into Madison Square Park, where the lawns face the tower and the original Shake Shack kiosk holds its permanent queue in the corner. Eat there if it's lunch. Eataly across the street is worth walking through whether or not you buy. Then south to Gramercy Park — the city's last private square, locked, key-holders only, and the joke is that you've come to look through the railings at grass you can't touch.
Walk Irving Place down to Union Square, where the greenmarket fills the north end Mondays, Wednesdays, Fridays and Saturdays. Time it for a market day and finish with cider; the trains all meet beneath you.
