There are a bunch of measures of nominal-nominal association.
There's the phi coefficient, the contingency coefficient (which I think applies to square tables, so perhaps not suitable for you), Cramer's V coefficient, the lambda coefficient, and the uncertainty coefficient. There are no doubt still more.
Many of them turn out to be a function of the chi-square statistic.
(If you have one or more ordinal variables, there are many other coefficients that are suitable for that situation.)
This wikipedia page lists the ones I mention.
I believe SPSS can compute the ones that I think match your rectangular nominal-vs-nominal situation - at least I am certain in the case of phi and Cramer's V and the lambda coefficient:
(Tables from here and here)