Lee Lowe has a blog on which are posted short stories. You can read Legacy as the first one. It's described as being fantasy and speculative fiction for teens and young adults, but I fancy there is a wider audience than that.
Well, this shows that there are now many ways to reach an audience for short stories. You can choose whether to run your own personal blog as a site for your fiction, and gradually build a readership; or you can participate in one of the many sites which permit you to post stories with lots of other authors, and which provide (one presumes) a larger audience ready-made. (To find the latter, Google "post your short stories" and you get over 1400 hits.)