I'm not american so i can't speak for that, but here in sweden some examples are Fisksätra in Stockholm, and Gothenburg (my fave city) has two northeastern lines of tram-centric suburbs that are just commie blocks in a forest, a similar slightly smaller suburb to the west which sits at the edge of the urban area, Jonsered which is a group of smaller apartment buildings way out in the forest with a commuter train station, and to the south there's a new area called Nya Hovås which isn't quite as removed from other stuff but still has the same feel of being a dense area surrounded by less urban area.

And at least the gothenburg suburbs are perfectly affordable since they have shiteloads of housing and are very much considered low-status areas. Also come to think of it, gothenburg has a bunch of natural (or at least still very pretty green park) areas throughout the city, so arguably many parts of the downtown area count as well.