I'm Board is an excellent game store in Middleton, which is not far from Madison. From downtown Madison you just drive down University. They have a board game night every Thursday that I try to go to when I can. I play Mage Wars there about every other Wednesday.
There is also a Pegasus Games on the west side of Madison, and a Netherworld Games downtown. The people at Netherworld Games seemed more focused on MtG from what I saw, but that might have just been when I was there. They certainly have board games in the store.
There is a board game club at UW-Madison, but you don't need to be a member of the university to attend.
There are also many people in the area that play board games, and have people over to play.
There is a fair amount of gaming in the area overall, and my recommendation is to go to I'm Board.