The use of "to" implies a definite destination for going: to school, to New York...
Without "to", the location is not specific: shopping, walking...
Twice a week, Max goes to the gym.
Twice a week, Max goes shopping.
If you know that Max is going to a specific place place, you can use "to". However, usually you know nothing about his whereabouts (otherwise you would not be asking), therefore you should use the more generic form, without "to".
The good thing is that the answer does not need to follow the rule of the question in this case. The answer will you "to" independent of the question.
Where does he go? (no "to")
He goes to the library. ("to")
Where does he go to? ("to")
He goes for a walk. (no "to"; the understanding is that he does not go to a specific place, unlike the question implied)