Seeing as you have sort of picked Oxford already. You could use that as a southern base. Warwick castle is not far OK the Queen doesn't live there but...
The White Horse at Uffingtnon worth a drive.
Strattford-on-Avon? if one is into that.
If not staying in Oxford itself use the park-and-ride to get into town it will save traffic and driving around a strange city looking for parking. There are three or four. I am only familiar with the Thornhill one the A40 just off the ring road Cream tea at the Randolf Hotel? Blackwell's Book Shop?
Forget Stonehenge. Might be OK to drive by but Avebury close by is more accessible if one is into old rocks.
Travel Lodge in Thame won't be full