While they seem like they ought to mean similar things, the present continuous and present simple tend to be used in different situations.
The present continuous is used for the specific action that is presently occurring, while the present simple applies more generally.
For instance, if someone asked me "What are you doing?" I would respond with the particular activity I was engaged in at the moment of the question. But if someone asked "What do you do?" I would respond with my job, or the thing that primarily takes up my time.
In the example in your question, "Where are you going?" is the kind of specific question you might ask when you're saying goodbye to someone, or if you run into them on the street. You would expect their destination to be the answer.
"Where do you go?" is unidiomatic, because it comes across as kind of existential without any specific time or activity added to it. However, "Where do you go [to do x]?" is a common formation that you might see if someone were to ask for a recommendation for a restaurant or an activity. Similarly, a question with time added is also common: "Where do you go on Mondays?"