It seems that sentences with мне and lacking a verb have an implied verb meaning something like "should". In another lesson we had «нам приготовить на обед» which was translated as "what should we cook for lunch", again missing a verb and with мы in dative.
I think of these sentences as having an omitted надо, so this one becomes «куда мне [надо]», ie "to where do I [need/should go]?"
How about "Whereto for me" [to go, to be]?"
It's obviously an idiom, which means that it's probably a shortened form of something which may not even be used any more. While mentally disruptive, idioms mean, for me, that I'm not going to understand the why or how immediately, if ever, and that I just have to memorize them. Asking for or getting explanations may be a lot harder and more time-consuming than simply remembering the idiom.
I constantly translate it to "excuse me" because "tell me" sounds rude which doesn't seem to be the intended intonation of this sentence. And that's not accepted either.
Google translate, translates this as 'tell me where I am' very much different from 'tell me where should I go'
It translates 'Tell me, where should I go' as Скажи мне, куда мне идти
Which should we believe?
BTW the google translate makes a lot more sense than this translation here on Duolingo.