Why isn't it אופה which was the suggestion?
Because איפה means location and not destination. You can use לאיפה instead of לאן, it is understood and as far as I know there is nothing wrong with it, but for some reason it sounds more colloquial and "street".
What would "לאן אתה דרך", which was one of the multiple choice options, mean?
it's meaningless, and grammatically incorrect. the literal translation of it is "where you road".
I read it as "darach" (thinking of it as a verb). Is there no meaning to the word in that form?
well there is also da-ra-kh (stepped on [something]) but it's still meaningless and grammatically incorrect in both English and Hebrew.
Isn't it possible to say "Lean holech ata? " ?
no, it is wrong sentence structure, it's a bit like "where are going you?"
לאן אתה הולך - why is it wrong??
Yucatan78 is right, it translates to "Where are you going?" with the difference that he used "אתה" instead of "אתן". It should be accepted.