Hi Amanda,
I am writing this with the assumption that you are an out-of-town visitor and haven't been to the LA Fabric district... be ready to be dazzled :-) Where to go depends on what you are looking for. The LARaqs article is an excellent guide for starters.
Some additional tips from my experience:
1. AZIPayless (see LARaqs article) has the best prices for chiffon at <$2.00/yard (45" width). They also have lycra and velvet -- however I haven't bought these types of fabric from them so do not know the price.
2. I have purchased swarovski buttons and swarovski trim at Gold Lea Trims at very good prices (someday I'll post pics of my costume in the "what are you working on" thread). It's a smaller store compared to the huge ones like Michael Levine's and Berger Beads, but has a good selection. No fabric, just trims and the like. The Persian lady owner is very pleasant and easy going -- tell her you bellydance and she'll be delighted :-) If you buy a significant dollar amount (~$100) you might be able to get a small discount if you pay in cash. If she's in a very good mood, she might give you a discount even if your purchase is just $10-20. See website for more info
Gold Lea Trims Home Page
3. The larger shops typically post discount rates for purchases of $X and above. In general, the smaller the store, the more likely you can bargain, esp if your bill is higher AND you pay by cash.
4. If you are looking for loose swarovski crystals and are not yet certain on what you want, Berger Beads displays their crystals in glass counters so it's much easier for customers to browse compared to Bohemian Crystal. I've not experienced negative customer service at either place.
5. Michael Levine's has a huge and excellent selection of fabric. They have a discount on a different type of item daily, so it may be your lucky day. There is an excellent selection of swarovski buttons/brooches/trim. They have silk fabric ($10-12/yard, 45" wide) which you can purchase to make your own silk veil.
6. If you are buying stretchy fabric, be sure to observe that the fabric is measured and cut with the roll lying FLAT. This might sound strange (yes, that is the correct way to do it after all, and most shops do so), but the following happened to me at one of the smaller fabric shops: the fabric was measured cut with the roll still standing vertically, and I ended up with a piece of fabric that was 1 yard on one end and 3/4 yard on the other. I didn't look at the piece I bought until 1/2 hour later and when I returned to the shop, the store person refused to cut me another piece to exchange. Just keep this in mind!
7. Practically all items in the fabric/fashion district are final sale: no refunds or exchanges, and no exceptions.
Have a very enjoyable time!