I just had a very good burger at Custom Burgers by Pat La Frieda. It's located in the food court of Terminal D at La Guardia, inside security. La Frieda is a longstanding meat purveyor, which explains the quality.
I built my own double burger. Good looking, isn't it? The meat was juicy and flavorful. It gave me the full-on burger experience, which is exactly what I was hoping for. A great way to start a flight.