I've had very few bad burgers in Wisconsin (they must really just know how to handle their meat here) and DLUX is another just very solid place to grab a burger in Madison. The atmosphere is sleek and open and usually pretty popping and yet is never too loud that you're not able to converse with your table mates. The DLUX Standard burger is a very good, as the name implies, standard burger with regular fixings, but my favorite is probably the mushroom swiss because I'm a total sucker for mushroom burgers. The fries are good and crispy and they have a good lunch deal where you can add fries for just a dollar more.
They also have a good drink special after 10pm - buy one get one free cocktails, tap beers, and wines. The Juni-Pear and Southern Charm are particularly delicious. They also serve food late so if after a couple drinks you get a hankering for a burger and fries, you're covered.