In Hammondsport, on lake Keuka, visit the Village Tavern. Good food, including burgers, great people. It’s right on the village square, a very pretty little town.
 
 
 

This isn’t a hamburger joint but the Roscoe Diner is sort a tradition on Rte 17(future I86). It is halfway between Middletown NY and Binghamton NY. It is easy on easy off the highway and a couple of gas station are next and across the street from it. I usually have breakfast they do a great deep fried french toast. The coffee is good and the bathrooms have always been clean when I have been in them.
P.S. I am sure they do a decent burger most diners do and this place has been around forever.