I shop at either Jo Ann's or the LQS. Jo Ann's does carry some really nice fabric in their designer collection. At the same time, I've seen some really thin not-so-good quality fabric at the LQS.
In general, I think that the LQS does have better quality fabric than anywhere else, but you need to discover that for yourself since you could be just as happy with a $7.99 fabric from Jo Ann's as you are with a $10.99 fabric from the LQS.