A Small Place exists at a strange crossroads between genres.
In many ways, it's a memoir; it seems to recount specific stories from Kincaid's early life in Antigua. However, any resemblance to Kincaid's actual life has been blurred through fictionalization—in fact, there's no explicit confirmation that the narrator is in fact Kincaid. We know we're grasping at straws on this one, but it's vague enough to bear mention.
In other ways, it's simply a piece of non-fiction about Antigua. The bulk of the book is spent describing the social and political history of the country, using real facts to bolster the narrator's arguments. For what it's worth, you're probably most likely to find this book in the nonfiction section of your local bookstore.
But there's enough fictionalization happening here that we can't define A Small Place as pure nonfiction. After all, Kincaid was never a tourist—that whole component is certainly made up, though also inspired by real life. In this way, A Small Place is a sort-of parody of travel literature, which typically promises to show a reader some new, exotic locale. Only instead of wanting you to visit, she just wants you to stay away.