In contrast to the oatmeal analogy, coffee starts going stale the second you mill it. The best coffee is ground up and immediately brewed. The longer coffee sits around milled the more it dries out and loses flavor/aroma.
I wouldn't recommend keeping milled grain around for a while. I milled some grain for an AG batch of Dunkelweizen at the homebrew store and life got in the way and it sat in my closet for a month in the plastic bags with wire ties. I brewed the beer and it was good, but not great. It was missing a depth of flavor I could only attribute to stale grain. My friends/family thought the beer was good, but I could tell it was not as 'fresh' as the dunkelweizens I had brewed in the past.
Moral of the story, if you are going to mill it and let it sit around, don't just leave in plastic bags with wire ties in your closet. Take measures to keep it fresh.