It's not entirely clear what information this old dinosaur is supposed to convey. Located on Seagirt Boulevard in Queens, it can't be a You're-Entering-Atlantic-Beach sign. You still have to drive another quarter-mile before you leave NYC, and then it's another quarter mile beyond that to reach the bridge that leads to Atlantic Beach.
There is a split in the road up ahead. By going right, you can take the Nassau Expressway south over the bridge to Atlantic Beach. Staying left puts you on the Nassau Expressway heading north, the way you'd go if you were trying to get to Manhattan. So perhaps the sign is simply informing drivers of two primary destinations that can be reached depending on which option they choose at the split. If that is the case, however, the sign would seem to be pretty worthless without any directional indications. (Drivers are not dependent on this sign for navigation; there are more modern signs located up ahead.)
Until relatively recently, there was another old sign of a similar size and structure located about 300 yards up the road. I don't know what it originally said; by 2010, there was a very faded wooden sign pointing the way to New York (meaning, presumably, Manhattan) that appeared to be nailed on top of the original sign. If you drive (or walk) by today, however, all you'll see remaining is a bent post that looks like it may have been hit by a car and decapitated.