Right on Capitol Square. Real nice Irish pub, the name means "badger den" in Gaelic. And if you don't know my now the significance of the BADGER in Madison, well then, I suggest your brush up on your history, or suffer the consequences at the next Wisconsin football game.
Didn't go here, but I have coworkers who have, and raved about it. Wide selection of ales, single malt Scotch, and Irish whiskies. Here they have pretty good pub food, and no matter where you are on the Square, this is not far from you. Sits directly across from the capitol.