You won't want to drive in Oxford. The drive (once you get past the perpetual delays on the M25 between the (M3), M4 and the M40) isn't too bad but parking in Oxford is atrocious. It is extremely expensive and hard to find on the street (to say nothing of the miniature parking bays which will earn you a very expensive ticket if part of your car strays over the line) and non-trivial and not cheap at parking structures. If you must drive there, then you are well advised to park out of town at the Park & Rides (there are several) and take the bus in.
In one day you will be hard pressed to do justice to both Oxford and my bit of the Cotswolds.
Of those places named previously in this thread - Burford has a fabulous wool church and a quite impressive high street (and the top is a lot higher than the bottom) but it is a distance from the others. Bourton-on-the-Water has the picture postcard views but also coachload after coachload after coachload of fellow tourists who often don't know why they are there. Stow-on-the-Wold is very nice and a local hub but is a relatively big market town and I think most people are looking for the views in a village. Moreton-in-Marsh has never struck me as very "Cotswoldy" and is a long market town.
If you will have a car I'd suggest getting into some of the villages. There are many, and it will depend how you tie them together.
You might throw a few of these into the hat - the Rissingtons, Long Compton, Upper and/or Lower Swell, Upper and/or Lower Slaughter, Broadway, Stanton, Stanway, Guiting Power, Cold Aston. There are many more.
Get out of the car and walk around.
But you can't do all that and Oxford in one day....
