In no particular order for Manhattan and Brooklyn.
The regular burger at Minetta. The black label is good, but for me the regular hits the spot just fine.
Minetta Tavern
113 MacDougal St, New York, NY 10012
(212) 475-3850
https://goo.gl/maps/3yTTeEcs7HP2
The lunch burger at Peter Luger.
Peter Luger Steak House
178 Broadway, Brooklyn, NY 11211
(718) 387-7400
https://goo.gl/maps/RKuXE1kv5wm
The lamb burger at the Breslin.
The Breslin
16 W 29th St, New York, NY 10001
(212) 679-1939
https://goo.gl/maps/SFKcUcVPB4p
The frenchie burger at Bar Bolud.
Bar Boulud
1900 Broadway, New York, NY 10023
(212) 595-0303
https://goo.gl/maps/zhUqtJdbzdD2
The cheese burger at JG Melon
JG Melon
1291 3rd Ave, New York, NY 10021
(212) 744-0585
https://goo.gl/maps/Pdn863tEJtT2
The cheese burger at Sea Witch Tavern.
Sea Witch
703 5th Ave, Brooklyn, NY 11215
(347) 227-7166
https://goo.gl/maps/1e56j9XGKCr
If you go Sea Witch you need to order fries and the pickle plate to go with.