When I run a contingency table NxN and I get a significant result with the chi-square test, is there a post-hoc test in SPSS to address the comparisons? Or should I run logistic regressions?
If you want to know in which cells are evidence of association, adjusted residuals can help you to understand the pattern of association inside the contingency table. In SPSS there is an option in "cells". See Agresti ("Categorical data analysis") for details.