driver8, you're essentially describing a particular pretext for a utopia. HG Wells'
Men Like Gods is an example of something very similar (people from this world are transported into a parallel universe that is better than ours in every way).
Otherwise, many such stories posit an isolated society (for example on an island, or at the poles, or inside the hollow earth) that has developed along the lines you describe, and now wishes to share its ways with the rest of the world, e.g.
A Traveler from Altruria,
Herland,
Islandia, or Aldous Huxley's
Island.