For the best burger place in Madison, I award it to Dotty Dumpling's.
In fact, they specialize in burgers and have a huge selection of them on their menu. Even if, in the extremely rare occasion, you blasphemously don't want one of Dotty Dumpling's original or alternative burgers, there is always the option to build your own.
Unfortunately, I cannot recommend my favorite burger here; it's because I tried most of them and was not disappointed each time I went. If you're in the mood for a heart attack, however, I'd go for the Melting Pot burger. Sometimes I get the Aphrodite burger in an attempt to falsely trick myself into thinking it is a healthier option.
Regardless, if you want a quality burger, head over to Dotty Dumpling's.