F&S Fabrics is the answer to your upholstering needs. Yes I've been scouring Los Angeles for some amazing fabric for my Danish sofa and have been coming up empty handed. I was feeling like I might never find something a)affordable or b)beautiful.
But then I went to F&S on Pico (just east of the Westside Pavillion). They have 3 home fabric stores on the same block of Pico so make sure you hit them all up. The jackpot is the 'outlet' store which is the one I pictured so that you definitely wouldn't miss it. Everything there is $10/yard or less and there are some good options.
Across the 3 stores, they have a fabulous selection of fabrics for sofas, drapes, tablecloths and outdoor furniture including tons of Sunbrella fabric. Everything is very organized (by color), the staff is helpful. And all of the fabrics I liked were $25/yard or less which is reasonable compared to some of the other prices I've found.