This guy likes Five guys, but I think, like Shake Shack, the nearest outlet is in Westport. That place on Delevan Avenue in Byram has my vote right now, but I’m open to suggestions.
UPDATE: GPD Folks mentioned “Big Top” some time ago and that, to my memory, was indeed the best. Blue and yellow roof, across from what was then Caldors (Walgreens, now) – it’s long passed, alas and is now an automobile repair shop. But my, their burgers were delicious – charbroiled, and fantastic onion rings.