I will agree with Gilley's, if you like a burger with thin patties.
Their double cheeseburger is drippy, juicy goodness on a bun.
Especially fun is watching the cook take a meatball of ground beef and throw it on the flat grill and press it down with his spatula.
Plus the fact that it is a late night haunt and an original 1940's Worcester Lunch Car (with a sliding wooden door) make for an interesting visit. http://www.gilleyspmlunch.com/
In Southern ME, a great choice is Wild Willy's in York ,ME, which does only grilled burgers, chicken sandwiches and milk shakes. http://www.wildwillysburgers.com/
In the Boston area:
R.F. O'Sullivan's, Beacon St., Somerville,MA is a small bar/tavern that takes near baseball size handmade patties and delivers them with hand cut quartered steak fries. It takes a while to get it to your table, but no one leaves hungry. http://www.rfosullivan.com/
A newcomer is Krazy Karry's in Arlington and Woburn,MA-another no- frills burger and milk shake only establishment. In the Woburn location, they are actually attached to an ice cream parlor. Juicy flame broiled burgers, 1/2 lb., over an open gas grill. http://www.krazykarrys.com/
In this area, there are many places that follow "guidelines" that indicate cooking nothing less than a medium or medium well burger. if you find a place willing to cook one to your tastes, you cherish it.