Hello! I kind of agree with patrickagaloos about wattpad. But, it's like the cliche saying of searching for a needle in a hay stack; one way or another, there are a few well-written stories to be found there.
Before wattpad though, I used to read original stories or fanfiction on livejournal or on fanfiction.net. The latter I still do to this day, in certain fandoms. Both had some real skilled and imaginative writers. Fictionpress is another good place. There's also a publishing house which has their own website for aspiring writers to post works that can be published, if it proves very popular... Just tried finding the link but I can't remember which publishing company it is On this site, you can read either the complete story or some chapters of pending or already published books.
As for actual published works, if you can look it up, there's a few free pdfs around that can be saved for reading either on or offline.