Yes, as many of us already know, the Census does not define "Urban" and "Rural", much less "Suburban". This article from the FiveThirtyEight blog attempts to use a survey to get to a working definition. Not their best work, but an interesting approach, none the less. The survey only includes about 2000 respondents, and there are over 30,000 zip codes. so not a very robust sample.
For those of you who want to cut to the chase, here are the rough break points they came up with:
Urban : > 2,213 households per square mile
Rural : < 102 households per square mile
You can read about it here: How Suburban are Big American Cities?