L.A. was the home of Woody Guthrie for a few years. Odetta lived there. One of the most knowledgeable people in the whole field of folk music lives there. Bess Hawes, sister of Alan Lomax.
McCabes in Santa Monica used to have folkie acts. This might be a good start. It's at 30th St. and Pico Boulevard. Check yellow pages for McCabes Guitar Shop.
There is an organization called Songmakers that meets in private homes. Check Alta Vista.
L.A. has been the home of the Dulcimer Festival and the Banjo and Fiddle Contest which used to be in Topanga Canyon, a rural suburb. Now I think it's held on UCLA campus in the summer.
There is a Riverside Folk Song Club which meets in the burbs which in L.A. can be a considerable trek. Practically nothing is accessible on public transportation unless you have half a day to spend.
Frank Hamilton