Well if you go to Duotrope they'll list over 1000 short story markets. If you confine them to the web based markets, all the markets they list will have stories available on line.
There is a little school of thought that web based magazines may not host as good a quality of story as print magazines. (I have no opinion there, just in case I get clobbered) Definitely making it into a print magazine seems to get a writer more respect. There are exceptions to this, eg Strange Horizons plus Orson Scott Card's Intergalactic Medicine Show. For the IGMS you do have to pay a small subscription to get to read all the story. Note, I know little about the short story world outside of fantasy and SF.
Another system I employ is googling the name of writers who make it into the top magazines and by that I mean the ones who pay pro rates. That way I get to find any story of theirs which is available on line. The way I see it, at least I get some idea of the standard of the competition. A new website Trabucco Road has a fair few stories up on line and the standard is supposed to be high although the pay is not.
Also if you Google short story writers you discover lots of them have websites with great short story links. So it takes a bit of hunting around but there is a wealth of information there.
If you are looking for sites where the primary focus is short story writing and critting is the primary focus there's loads of them out there too.