Hello Bunbry and welcome to WW.
It's always hard with short stories, unless they suit the mags (It's hard then too, of course, but at least you know what you're aiming at. As well as the JWB link you could try here, which is a sortable database:
http://www.duotrope.com/index.aspx
Small mags come and go - even the relatively big ones like The London Magazine can lose their funding. There's Ambit and Glimmer Train and Anon, that I can think of off the top of my head, Comma do anthologies, as possibly do Salt (not sure about that?)
And then there are the competitions - Fish in several varieties, Bridport, Asham's women only, as is Mslexia but they have excellent listings, which they can't stop blokes reading, also I think The New Writer has listings too.
Emma