Echoing @thetopher about Archive of our Own (AO3). Also, if your story has a specific pairing, there are often specialized websites for that, too. For example, I'm a member of a site for Spike/Buffy fanfic. There are a ton of those for most pairings. But if it's Gen (general/no specific pairing), then definitely Archive or Fanfiction.net.
If you post your story on these boards then you want the Introduction to the Watcher's Diaries forum which is down in The Slayground section on the main page of this site. Otherwise - what everyone else said about AO3, though the Buffy board on Fanfiction.net is also quite busy. Lot's of people post on both.