I gut em where they fall.
If I didn't use all of the meat myself, I would be inclined to donate it to a food bank or homeless shelter....
But, I eat every little scrap I can get (except the heart, liver, etc). I don't eat these because they are apparently high in contaminants and I just plain don't like 'em. However, I did give away a doe's liver last year to an old friend. Rather than wasting precious meat, give it to someone who will appreciate it. Perhaps it is more a matter of laziness than not wanting the meat. Show some respect for what you hunt and use every bit of it that you can - or give it to someone who will.
Oh, and gut em where they fall - unless it is really cold out and you can get em out of the woods and hanging super-fast.