You have it backwards actually. You need to walk further into the cities to see the really poorly-educated.
Here’s the actual data. Look at Illinois for example. All the rural counties are right around 8% functional illiteracy. Then Cook County (Chicago) is literally double at 19%. The trend seems to repeat in every state. Queens and Brooklyn are the most illiterate parts of NY, while far-away Ontario County is the most literate.
The only real exception is in the Southwest. California’s most illiterate county is rural Imperial County with a whopping 41% illiteracy because of all the immigration.