SoundCloud to host the file and then embed into a blog post. SoundCloud is easy to use although free accounts are limited to 3 hours (per month I assume, as the site does not say) and a 5GB file size max.
As a test, I have uploaded and embedded a recording of an interview I posted back in May of last year. The interview is with Amy Briggs about using a game in an upper level biology course. The recording quality is not that great as there was mechanical noise in the background, but hopefully this will lead to more and better audio in the future!