I have not been there but there is a proper campsite called Eau Rouge right next to the circuit. I think there may also be another nearby. We have often thought about adding the Spa GP to our list but have not quite got round to it.
We've stayed there five or six times for the Spa 24 hours but never for the GP. It's a nice campsite, the facilities are OK not fantastic but perfectly acceptable. For the 24 hour they usually put the motorsport bods on the overflow field which personally I prefer to the look of the main site.
I don't know what you are referring to as the official campsite, for the 24 hour (and other events I've been to), there are numerous other camping areas, the biggest probably being at Les Combes which is at the end of the Kemmel Straight at the top of Eau Rouge (for the anoraks it's the point where the old circuit heads off into the country towards Stavelot). Les Combes is on a pretty big slope (even by my standards!) and certainly for the 24 hour has no facilities and you'd expect it to be fairly rough and ready.
There are lots of other private campsites that spring up for the 24 hour and I suspect that there are even more for the GP.
There is also a site nearer to Spa town itself Spa d'or I haven't stayed there but I have friends who have and they liked it. However, Spa town is not where the circuit is, the Circuit is at Francorchamps which is a few miles from Spa itself so you'd need to make sure of any arrangements for parking at the circuit etc.
Personally I would stay at Eau Rouge camping if you can get in, you may find it's already booked but it's worth a try. The site is Dutch run and they speak OK English usually and will respond to email.
If you've got a link to the official camping you're looking at post it up and I'll tell you what I think about it's location. The problem with all GP's is either being close enough to walk/cycle or being able to make sure you can get parking at the Circuit.
Amazing family weekend with old steam engines, classic car displays, market stalls, and full catering and bar. And camping on site - Save £25 by booking in advance.