The District spans several city blocks and is wholly dedicated to fashion and fabric, both wholesale and retail.
(You can find a list of all the fabric vendors here.)
Nearly every shop has a host of fabrics -- furs, vinyls, upholstery, dance & swimwear, brocades, silks, wools, and so much more. There are literally piles of fabric pretty much everywhere -- as far as the eye can see. There are even a few 'tours' hosted by the local costumer guilds. A full day of fabric shopping will only give you a taste of what is in the District.
Many a costumer designer for movies will come here to source their fabric for their creations. One of my favorite stores sourced some of the fabric for a specific movie -- cough The Force Awakens cough -- although he is bound not to disclose that too publically.
Some of the shops are small, piled floor to ceiling with fabric, where you can get fabric for as little as $1.99 And some, like Michael Levine's, are much larger stores, where you pay a little bit more.
Levine's will also sell you fabric by the pound, if you want.
It's also just not fabric. There are sewing supplies, notions, buttons, trim, beads, and anything and everything having to do with sewing. We might have picked up a few things, besides fabrics.....
If you love to sew, costume, make, or create something out of fabric, I highly recommend going to the LA Garment District. Just bring a friend to share the oohs and aaahs. Wear good walking shoes. AND bring a list of fabrics that you need, otherwise, you might just get a touch bit overwhelmed.