...is not in Manhattan; it's in Brooklyn. Right over the Williamsburg Bridge. You already know what I'm going to say... it's Peter Luger's.
This is not your fancy, trendy, upscale type of place. It resembles a local pub more than the most trusted name in steak. The service isn't particularly wonderful - the waiters are surly at best. Bring a group of people and a fair bit of cash, as they don't take credit cards.
I'm partial to the Bacon strips at first, and my father (a long time Luger's patron) goes for the lamb chops with the same tireless review that they are so tender they almost melt in your mouth.
Asking for a menu is unnecessary. Order by the number in your party (e.g. Steak for 4) and wait with bated breath for the best steak you'll ever have.
You can also get their house brand steak sauce at several supermarkets in the area - you'll never use A-1 again. Just don't ask surrounding steakhouses if they have Luger's sauce for their steak. The don't think it's as funny.