Though this question is a topic of heated debate, here are some of my picks:

1.  Big Nick's.  They have A LOT of different burgers to choose from and mostly all are under $10.

2. Burger Joint. So this place isn't exactly "secret" anymore, but it's still cool to wander in Le Parker Meridien and all of a sudden find this hole-in-the-wall burger place. The vanilla milkshake is also excellent.

3. Rare Bar & Grill.  A burger is lonely without fries, and at Rare there is an entire French fry tasting basket to partake in.

4. If you want to truly indulge, DB Bistro Moderne's DB burger with foie gras and truffles is about as rich as it gets.