Burger joints abound in Denver, so narrowing down your choice of where to celebrate National Cheeseburger Day (Sept. 18) may be difficult. This list guides you to some of the best restaurants for burgers (and a veggie burger) in the city today. And holiday aside, you can get these tasty burgers almost any day of the week. My Brother’s Bar The burgers at My Brother’s Bar are classic as the establishment itself.