The Fashion District is located on the east side of downtown Los Angeles and stretches for blocks and blocks in the vacinity of, and hardly limited to the area around, Olympic Blvd between Los Angeles Street and Maple. If you exit the 10 freeway on Maple there is even a sign stating The Fashion District. This will include the infamous "The Alley". You can find anything here - children's clothing, men and women's clothing, suits, shoes, fabric, notions, bridal gowns, bridal fabrics, upholstery fabrics, purses, sunglasses, luggage, costume jewelry, etc. - and it's all discounted.
If you live in L.A. and you don't know this area, shame on you!
If you're planning on visiting L.A. you've got to try to make it to the Fashion District. I haven't been in a while but I just drove through it on my rediscover L.A. venture. I'm not saying it's all designer clothing and designer outlets but you never know what you might find in the Fashion District and there is a little bit of everything for everybody. And if nothing else it will definitely be an experience.
Feel like shopping? Remember The Fashion District and I'd suggest leaving early unless you don't mind being in the midst of the crowd of people you'll run into.