I believe the SF draw takes place on Tuesday evening, immediately after Sussex v Glamorgan on Sky (there's no reason to wait until the QFs are played first).
Right now there are nine possible teams who we could face, and I would argue that Durham are the weakest, and Notts the strongest, of those sides.
I would imagine we'll be the SF which Sky choose to show, for the simple reason that their cameras will already be there for the ODI the day before.