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.