Is there a widely-accepted opposite of "as the crow flies"?
By road would be a natural choice, as opposed to "in the air" implied by the crow.
It even has a dictionary entry and example:
by road
In or on a road vehicle.
Lying just inside the official boundary line between the two countries, Gretna was about 350 miles by road from London.
— Oxford
(The distance between London and Gretna Green is around 270 miles as the crow flies)
Not an answer in the strictest sense of the question as I could not think of a common idiomatic alternative to "As the crow flies". However, a nicely balanced and easily understood alternative would be "As the road winds".
Updated to add that "As the road winds" is found commonly in text so while not strictly idiomatic it is not simply made up either.
"As the road winds", Google book search
It's five miles as the crow flies, or twelve as the road winds.
As the wolf runs maintains the same structure as the original phrase and conveys the meaning of distance on the ground. It's not a particularly commonly used phrase, but some searching did turn up some support that this is something that has been used before.
Tolkien makes use of this phrase in The Lord of the Rings.
'How far is Moria?' asked Boromir.
'There was a door south-west of Caradhras, some fifteen miles as the crow flies, and maybe twenty as the wolf runs,' answered Gandalf grimly.The Fellowship of the Ring, Book II, chapter IV: "A Journey in the Dark" — J.R.R. Tolkien