How does the setting of rural functions in this book? What values, such as virtue or peace, does the rural demonstrate?

This is a tricky question, as The Importance of Being Earnest is a satire that seems to poke fun at all its characters. The three-act play takes places mostly in the rural/country setting. The first act is set at Algernon's flat in London, and then the action moves to Jack's country estate. Upper-class citizens of England in the Victorian Era (and earlier times, too) often had homes in both the city and the country, so they could spend time with people and entertain according to the social calendar. The society in city and country would differ, of course, and in many works of literature, a rural or country setting is associated with innocence and peace. On the other hand, the urban setting is more bustling, more corrupted, and more sophisticated. In the play, we see that the two main female characters—Gwendolen and Cecily—have been brought up mostly in different settings, and this affects their characters. Gwendolen is a city dweller and sees herself as more experienced and refined, while Cecily has lived a rather mundane existence in the country with mostly the company of much older people. Her lack of social sphere seems to lead to her overactive imagination (like inventing a relationship, complete with broken and rekindled engagement, to an imaginary man).
However, when Gwendolen and Cecily meet for the first time, and discover (or so they think) that they are engaged to the same "Ernest," they begin hurling insults at one another. These insults reveal that both city and country values are satirized by Oscar Wilde. Take, for example, this exchange:

Gwendolen: I had no idea there were any flowers in the country.
Cecily: Oh, flowers are as common here, Miss Fairfax, as people are in London.
Gwendolen: Personally I cannot understand how anyone manages to exist in the country, if anybody who is anybody does. The country always bores me to death.
Cecily: Ah! This is what the newspapers call agricultural depression, is it not? I believe the aristocracy are suffering very much from it just at present.

Here, Gwendolen exhibits startling ignorance for someone who considers herself sophisticated. Cecily hits back with a dig about "common" people in London, which is meant to degrade Gwendolen's sense of superiority. At another point, Gwendolen brags that her mother has brought her up to be "short-sighted." Clearly, Wilde is poking fun at how condescending city people can be, thinking those in the country are less refined and educated. Cecily, though, is also naive and silly.
Beyond that, Miss Prism and Reverend Chasuble, both supposedly educated people, dwell in the country and are surprisingly idiotic themselves. They have no social skills and have a hard time communicating with one another. Chasuble claims to follow the rules of "the primitive church" regarding marriage, even though England has not been "primitive" for centuries. Both characters are bumbling and seemingly somewhat incompetent. Therefore, it's clear that Wilde is not automatically holding up the country and its people as beacons of light or innocence in a corrupt London. In Wilde's play, everyone is made fun of as part of his satire of the English upper class.