Grand Central is one of the few big New York sights that's genuinely free, genuinely open, and genuinely quick. You don't need a ticket, you don't need to queue, and if you give it 45 minutes you'll have seen the parts that matter. It sits at 89 East 42nd Street at Park Avenue, on the southern edge of Turtle Bay, which puts it about a mile straight down Lexington from us on East 62nd Street.
Most people walk in, take a photo of the clock, and leave. That's the version we'd skip. Below is the order we'd actually do it in, including the two things almost everyone misses, and where to eat once you're inside.
Go on a weekday morning if you want the rush-hour scene, which is the real show. Go on a Sunday afternoon if you want the room mostly to yourself and space to look up without getting shouldered. The main concourse is at its best around 8am on a weekday, when the light comes through the south windows at a low angle.
Getting there from the East 60s
Walk south on Lexington and it's around 25 minutes from East 62nd Street, all flat, with Bloomingdale's at 59th on the way. Faster: take the 4, 5 or 6 from Lexington Av/59 St down to Grand Central-42 St, three stops on the local. The 7 and the 42nd Street Shuttle to Times Square both run from inside the terminal, which makes it a useful hinge point for the rest of a day.