Typically they move deeper until water starts cooling (September) at which point they move shallower again and slowly toward spawning grounds. As for exact locations, that's somewhat of a mystery, but the GLATOS program launched in 2010 sheds some light on that.
Interesting discussion actually, I remember some old-timers arguing about whether walleye start "staging" the spawning grounds before winter. Some guys said they do, others said they don't. Well, GLATOS proved that walleye certainly do start showing up in spawning grounds as early as September (although not in large numbers). I'm curious whether the fish are there to stage, or they just happen to be swimming around...