I'm more familiar with classic than contemporary ones. O. Henry is loved for his short stories, which have a wide range of topics. Two other Americans, Edgar Allan Poe and Stephen Crane, wrote classic short stories (Poe with a gothic or horror theme; Crane's Open Boat is recommended). James Joyce's classic Dubliners is a collection of great short stories set in Ireland. There are many others, but these few popped to mind.

Alice Munro is a good start. A recent Nobel prize winner in literature that won for short stories. Hard to beat and many of her stories are available for free online where they were published by magazines like the New Yorker. She is a modern master of English literature. No old-fashioned words and phrases.

David Sedaris' collections of essays/memoirs are very enjoyable, at least in the audiobook version.

You may want to look up something called "flash fiction" which are very short stories (usually 1,000 words or less). You can find a variety of them online. For example, you may want to check out a website called 101words.org, which shares short stories written in 101 words or less.

Do you want to read Children's stories?