First, stay away from the downtown jewelry mart. There are some good vendors there, but you are more likely to get fleeced if you don't know what you're doing.
I moved out of LA about 8 years ago, but the place where I got my wife's engagement ring is still around:
Wayne Jason Jewelry Designs
105 W. California Blvd., Pasadena
(626)795-9215
They are not a discount outfit but they do have some nice original designs. Their service is very good. When one of the side stones fell out of her ring 10 years later, they gave us a replacement for cost even though they hadn't seen the ring since I bought it and we had not been getting it professionally checked for damage.
In general I agree with Lawgem about the LA Jewelry mart. That said, I just had my new diamond appraised and set down there.
Charles Carmona from Guild Labs did the appraisal, and Dan at Navalty (sp?) jewelers did the setting. Both seemed honest, straighforward, and knowledgable, and I seem to have gotten good value for what I was looking for. (I bought a stone off the Internet and had them receive, evaluate and set it). I found them through references. I never would have found them by wandering the street level.
What did Charles Carmona charge for the appraisal (and for what size diamond, since some charge according to ct weight,) and could you email me his contact info?