You can debate whether or not this is technically "urban," but the
neighborhood of Kenilworth here was developed in the 1920's, so by American standards it's oldish.
Why is it relevant to this discussion? Because when the developer bought the property he let a horse loose on the land and followed it, marking the routes it took around the property. He then used those routes to lay out the streets, on the principle that a horse would know the most efficient ways to traverse the lay of the land. You can't really get any more organic than that when it comes to planning your streets.
Fun fact: The centerpiece of this neighborhood is the Kenilworth Inn, once a glamorous hotel that was confiscated by the US government during World War II for use as a hospital. Afterward, it was converted into a mental institution and then later, expensive apartments. While in use as a mental hospital, it was one of the institutions where the lobotomy procedure was fine-tuned and ultimately perfected.