Next door is properly placed. It modifies the guy, so it's part of the subject NP.
If you move next door it becomes a modifier on something else.
I was thankful for the guy shoveling snow next door from my driveway—next door would probably be taken to modify the predicate, designating the place where he performed the shoveling; but it might modify snow, designating the snow's location.
I was thankful for the guy shoveling snow from my driveway next door—next door would probably be taken to modify my driveway, designating the driveway's location.
It's very unlikely that either the snow or your driveway is next door, or that your neighbour was shoveling snow off your driveway there.