What you are looking to do is pretty common in statistics and is referred to as correspondence analysis.

My first stab at analysing data is always to perform PCA (Principle Component Analysis) on it. However, PCA is only applicable if your data can be assumed to be continuous in its domain. I don't know much about stepwise regression, but I found a paper on an extension of PCA to categorical data here: http://www.dm-lab.ws/www/contents05/covEigGiniRep16.pdf .

Furthermore, if you are looking for a stats package that can perform correspondence analysis, R does it and is freely available: http://www.r-project.org/ .

I found a disussion on correspondence analysis in R here: http://www.jstatsoft.org/v20/a03/paper .