Have you thought of subscribing to one or more of the many magazines that publish new authors (as well as established). Fantasy is more limited (Fantasy & Science Fiction and Lightspeed are the two I'm most familiar with & like). I'm less of an SF fan, but there are definitely quite a few offerings (Dell has a number of well-regarded ones like Asimov's).
The earlier year's best anthologies suggestion is also a very good one.
Happy hunting, and let us know if you find any less-known gems!