I wouldn't be surprised to find some suburbs with some of the traits you mention, but it hasn't been my experience with them. I've lived in about 5 different suburbs in my life and a supermarket has never been more than 2 miles away - certainly not a 20 minute drive and it's even within biking distance. Parks are by schools and there's usually an elementary school fairly close if you're looking to do something with your kid. Depending upon the suburb you can also play in the street, which I regularly did growing up.
The traits you are talking about sounds more like a rural area than a suburban one.