Regression analysis allows you to establish causality between variables, whereas correlation only indicates whether variables related or not. What is your goal?

With distance "as is" you are looking at a linear regression. However, if you transform it into "brackets" your DV would be on the ordinal scale. Therefore, you will be looking at a completely different model (e.g., ordered logistic regression). Now, when you say MLR -- do you imply multinomial logistic regression? If so, then it deals with categorical predictors, not ordinal.

Why don't you run an ANOVA with a continuous DV and two categorical predictors?