The cashier will most likely use keigo, the super-polite language that "inferiors" are expected to use toward their superiors, in the world of business and commerce. In keigo, are you eating here usually translates as "Kochira de meshiagari desu ka?" (kochira = here, meshiagaru = eat / drink) or "Tennai de meshiagari desu ka?" ( tennai = 店内 being "inside our shop")
Ai-chan, the assistant manager of my school when I first moved here, told me to say "Koko de" (lit. "here") for dining in and "Omochi kaeri' (lit. carry home) for takeout. I used it and it worked. That weekend I told my friend Ben about it and he used it a few days later. For both of us it was one of the most exciting linguistic experiences we' had up to that point. Actually saying something and seeing the dawn of comprehension in another's eyes.
I guess it'd be nice and polite to put in a "kudasai "at the end of the sentence.
More recently, I've been seeing "takeout" as a katakana phrase.
|"takeout menu" in katakana|