I hunt north central Ohio, and we kill a lot of rabbits along the edge of cut corn fields in the grass. Some of it doesn't even have to be high grass. We've probably killed 40 or so like that this year. The only time you'll most likely find them in the corn fields is at night...judging by the amount of tracks.

It's funny...this year we've killed most of our rabbits away from thick cover. I killed one that was backed up to an old apple tree in a mowed orchard. When he took off, I was NEARLY too startled to shoot him.