It's not so common to contrast the country to the wilds, nowadays, but The Hobbit has the Arcadian Shire next to the wilds that Bilbo and the dwarves set out in. The Wind in the Willows has the bucolic River and the Wild Woods. Used to be a much commoner trope. In the early 19th century, a landscape was beautiful only if fields or pasture, perhaps with a village or town or even city in sight. Wild land could be picaresque, or sublime, but never beautiful. When the first tourists headed toward America, they scuttled from city to city to see the buildings and institutions there; the only rivers they might travel down were the Connecticut and the Hudson, both of which had heavily farmed banks. When that's the contrast, you tend to get the law-abiding shepherds and farmers, versus the desperate outlaws of the greenwood -- Toad and Rat and Mole vs. the weasels and stouts. But often it's the uninhabited nature of it -- the wasteland. (If you find it incomprehensible that they would really regard it as a waste, think of the arguments that there must be intelligent life elsewhere, or so much of the space in the universe would be wasted.)
The outlaw vs the law-abiding is much more common when the wild's contrasted with the town and city, which are lumped together for that contrast. Especially if they feature the royal court. To be sure, it can be the brave, stout outlaw fleeing corrupt law and injustice and praising the wilds for its freedom. The Duke in As You Like It, for instance. (And there the country is assimilated to the wild; Rosalind buys some sheep pastures for her refuge.) On the other hand, it can be the law-abiding, orderly life of city and court versus the brutality of the outlaws. Taran runs into vicious outlaws in The Chronicles of Prydain. If, on the other hand, it's not outlaws but those who live in the wild, you may get into the barbarian virtues, the toughness, the courage, the hardiness to live in the wild. Or they can just be barbaric. Conan the Barbarian once fought against the barbaric Picts on behalf of civilization, though his speech at the end says that civilization is ephemeral and barbarism the fall back.
The contrast between country and town, or city, gives you the pleasant green rolling hills, bedecked with trees and flowers against the overdecorated and choked town. Or perhaps the dreary, falling down houses on a monotonous landscape in contrast to the pleasantness and decoration of the city. This leads into the simple, hard-working, honest, loyal country folk and the deceitful, intriguing, fickle city folk. Or, conversely the educated, courteous city folk versus the narrow-minded, dull, incurious country folk who believe a bride from the next village is a furreiner. The former trope is the common one nowadays, probably because urban living is so commonplace. It was less common when there were fewer cities, but not unknown -- probably because writers were more likely to live in them, even then. That's where court was, after all. You get both the Shire and Gondor in The Lord of the Rings, and while both come off well, there is an element of the hobbits having fewer manners and more frankness than those of the city. Jane Austen touches on the contrast in Pride and Prejudice, when the smallness of the neighborhood is touched on, compared to any city. In Northanger Abbey and Persuasion, even though part of both novels take place in Bath, there is only some, but there is some: Catherine finds much to turn her head with frivolity in Bath, and Anne is grieved that Elizabeth is so proud of her small home, where she spends her life in entertainment, and that the Admiral and his wife, having taken the hall, are no doubt looking after its poor as well or better than Elizabeth ever did.
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