So let's take a look at this sentence:
There's a supermarket there.
This sentence, of course, doesn't mean "A supermarket is there there," which wouldn't make any sense. This is because the two theres in that sentence are playing different roles. The first there is a dummy there; it's just a marker used as a subject, here in the so-called "existential construction." The second there is a locative there, referring to a particular place (Huddleston & Pullum (2002), p. 1391).
Note that we can usually replace the locative there with "in that place," since the two mean roughly the same thing: "There's a supermarket in that place" means roughly the same thing as "There's a supermarket there." But the dummy there often can't: "In that place is a supermarket there" is unidiomatic and would likely mean something different.
Notably, a dummy there can only ever be a subject (or "raised object"; ibid., p. 1391). So, in "A supermarket is there," the there can only be a locative there. But, in "There is a supermarket," the there is likely to be interpreted as a dummy there. In other words, only "A supermarket is there" unambiguously specifies the actual location of the supermarket; "There is a supermarket" just asserts that the supermarket exists.
In the context you specify, the two mean roughly the same thing. "There is a supermarket" would be interpreted as "There is a supermarket in the town." "A supermarket is there" would be interpreted as "A supermarket is in the town." Those two, of course, amount to the same thing, since both assert the existence of a supermarket located in the town.
However, in English (as a general rule) we tend to prefer to put new information later in a clause than old information (ibid., p. 1372). Since "a supermarket" is introducing a new entity into the discourse, "There is a supermarket" would generally be the more idiomatic choice.