It's not a matter of being considered a secret. I don't have to answer the question because I don't want to. No other reason is necessary. Refusal to answer does not create reasonable suspicion, which is the standard the police must use.
If one were drunk, any DWI attorney would tell you shutting is the most prudent course of action (not that I have experience with that, mind you). Shut up and hand over your license, insurance and registration if applicable. Those are the only things the police are entitled to.
The reason I suggested the particular question that I did was that, to the extent that DUI checkpoints are allowable at all, they are predicated on a cop's authority to ensure that people operating a vehicle are able to do so safely and competantly. While even competant drivers get lost, effective travel typically requires knowing something about one's route and paying at least some attention to one's whereabouts.
While it may not be quite as informative as things like the line-walking test, asking a sober driver where he is would seem to be a way of determining his sobriety in most cases without requiring him to leave the vehicle or reveal anything that could even potentially be personal.
The correct answer would be, "Yes?"