Duo does accept "Is there any store around here?" now (8 May 2019). Thanks if you reported!
EDIT: But, after going further in this lesson (Travel 5), I think Duo wants us to learn that this kind of question is asked one way in Spanish (alguna tienda) and--usually--another in English (any stores). I now think my first translation of this sentence inappropriately forced the Spanish into the English pattern. 15 May 2019
To expand on what Bryce shared... In English when we use the word "any" we can always make the noun plural, but in Spanish, when asking about an unspecified amount of something, when looking for one or a very few of the item, a singular noun is used. For example, "Do you have any books" could be translated as "Tienes algúnos libros?" when the expectation is that the person may have many books. Whereas, asking "Do you have 'a'/'some kind of' book?" would be translated as "Tienes algún libro?" From the link lambisqueiro shared: http://www.spanishdict.com/translate/any (scroll almost half-way down the very long page to the section on "any" when used as an "adjective in questions"): "When [any] modifies a plural noun in questions it is often not translated. However, if a low number is expected in response, [algún]/[alguna] + singular noun is used". Visit the page to see example sentences for this. Likewise, when in the negative (there aren't any), ningún/ninguna + singular noun is used.
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Maybe so, but it seems a bit colloquial to me, and more of a spoken language. The words round and around, sounds very similar, but in written form I think they should have separate spellings since they have different meanings (although related). Just like it's and its'. The circle is round, and its' circumference is around it. It's true, isn't it?
Olof, no such word as its'. You mean its.
Barbara, you asked this same question twice, a month apart. So, you may still be puzzling about it. I believe the answer is that Duo's prompt question is asked one way in Spanish (in the singular) and another in English (plural). Both Brycecrab and katiebdenver have posted useful explanations, above. Duo also includes the current question as an example in the "tips" for the Travel 5 lesson: https://www.duolingo.com/skill/es/Travel-5/tips
how is it possible that my answer, is there any store around here? ... is wrong?
OK, i get it now..... Are there any stores around here?.....or .....Is there a store around here? are correct. Is there any store around here? ... is incorrect, although it is commonly spoken in English. Point being, we are learning Spanish and English has 14 quazillion ways of saying things. I more often than not get the Spanish right, and the English wrong......