An example of the kind of congressional districts that I would like to see...keeping in mind never to break up a county when forming any kind of electoral district.

Seriously, though. My solution to gerrymandering is as follows:

Rule #1: Don't break county lines to form a district.

North Carolina has 13 districts and 100 counties. 

That leaves 13 districts with 7 counties each and 9 counties left over. That means 9 of the 13 congressional districts would have 8 instead of 7 counties.

Form the districts so that the districts wit the least population have the most counties.