You're leaving it so late that I think you'll have a hard time to find anywhere near the circuit and will have to travel in ...........

Yep! Looks like I'll sleep in the car...

I'd forgotten about this query, at the time my German hotel finder was down. For that weekend http://www.hrs.com have found a selection of rooms still available

closest :14 miles at £145 per night (double with breakfast)

cheapest: £45 (double exc. breakfast) 26 miles away.

and a variety of prices and distances in between. If you're still looking give them a try, their normal business terms are that you pay the hotel once there but for that weekend the hotels may want a card number to charge if you don't show. Use the location Rennstrecke - Nürburgring

Thanks Steve8482 for your help.
In the end, I'll be staying at a friend's relative in Cologne.
Leaving tonight, can't wait