Accommodation at any Gamefair is always snapped up early; you need to be booking now.
Nowhere in Oxfordshire is what you'd call cheap; but the standards are pretty high. We stay here when the Fair is at Blenheim
The Forge in the village of Churchill. Clean and tidy, excellent breakfast, nice people, own bit of parking. Quiet village.
There is a first class gastro pub, The Chequers, the other side of the village street.
It's about 30 minutes drive from the Palace, and
lagopus is right you need to be early to avoid queues. From the Forge you can travel on minor country roads avoiding the traffic until you get right into the Woodstock entrance. Some years they have another entrance that you access off the minor road ... it's a doddle then.
Regards
Eug