PCA-like analysis for dataset that has both categorical and continuous variables
I'm not aware of any the dimensionality reduction algorithms (like PCA) that can work with categorical values.

However, an approach that could help you with that is to make a one-hot encoding of your categorical variables (if the number of possible values is manageable. Otherwise, try to pick only the most frequent values and assign the rest to a single variable). 

If you are using Pandas DataFrames, get_dummies can be helpful.