Large categorical dataset for regression
I would like to recommend to check the following open data repositories and meta-repositories (they are not focused on categorical data, but I'm sure that many data sets, listed there, contain such data):


http://www.kdnuggets.com/datasets
http://www.data.gov
http://www.datasciencecentral.com/profiles/blogs/big-data-sets-available-for-free


Also check built-in data sets in the open source software Parallel Sets, which is focused on the categorical data visualization: https://eagereyes.org/parallel-sets.