Basically this, though not exactly the same:
Urban: NJ, NY, MD, DE, MA, CT, RI, NV, CA, OR, WA, AZ, UT, CO, NM (to some extent), KS (to some extent), TX, MN (the Twin Cities and suburbs compose about half the state's population alone), MI, OH, IL, VA (though it's more suburban in some ways), GA, NC, FL, AK (look at Anchorage), HI (in some ways).
Rural: ID (kind of - the Boise area is expanding and soon ID will be a split, but right now it isn't quite), MT, WY, ND, SD, NE, OK, MO, IA (arguably the most stereotypically rural state along with those in the Great Plains), KY, LA, AR, TN, MS, AL, IN, WV.
There are probably a few I forgot. (Obviously I skipped some states, because not all are fully 'urban' or fully 'rural', SC among them, but I might have forgotten some urban states and some rural states in this list.)