The standard initial market for a short story is a literary magazine. Famous examples include The New Yorker for literary fiction and poetry. For science fiction and fantasy genres, notable options include Fantasy & Science Fiction, Asimov's, and others. As a general rule more prestigious magazines are able to be more choosy on what they end up publishing. Beyond some of these few links, there are tons of places to find magazines of all sorts to submit to:
- Writer's Market is a yearly publication with a subscription website you can check out
- Ralan's is specifically geared towards science fiction, fantasy, and humor
- Duotrope has some great search features for their database of publications.
From these magazines it might be possible that your short story could go on to end up in something like Pushcart. There's also the annual Best American Short Stories. You can look into short story contests (even narrowing the search to science fiction short stories only).
There are lots of options. Just don't get discouraged by potential rejection letters along the way and keep polishing, editing, revising, and submitting.