Green Valley is on the mostly West, some South, side of St George. There is a hill you have to go around such that there has been shopping and restaurants built out in that area giving it some of its own independency. However, it is part of Greater St George as it is close enough for people getting to work and that kind of thing. It is on the same side of Greater St George as Snow Canyon, Ivins and Santa Clara. However, it is not typically as far out as those areas, but more southerly of the hill the current airport sits on. Here is a link off the maps links on my website of a St. George Google Map from which I will help you identify the Green Valley area. If you can see where it titles Santa Clara and zoom in one notch. Then more closely you are looking for W Sunset Blvd. From there you will see a road that runs south called S Dixie Dr. Green Valley is everything along that road, just south of W Sunset Blvd. It includes, but not by name, the Sunbrook area. You can hit hybrid or Satellite on that map to see the hill you have to go around to get to Green Valley West and south of St George.
There are some nicer areas in there with new roads not shown on the map. Also there are a few older areas. It is a smattering of upper class, a lot of family housing, few apartments, also retirement condos and some exclusive housing, not just Sunbrook.
It also hosts one of Ence Constructions developments called Olive Grove.
Green Valley also has the resort condos: Sports Village and Green Valley Resort. The unique features here are weekly and monthly rental capability or just own as second home/condo or vacation get away. These have a few more amenities with higher association dues.
You can also see more information about Sunbrook and where it is located...