Oxford is an easy drive from the cottage taking you along the A3400 through Woodstock. Woodstock is where Blenheim Palace is and you might like to stop off there although, in my opinion, the palace is really worth a whole day out in itself. Woodstock itself is an attractive town (turn left just after the pedestrian lights for the car park which is hidden away off a narrow street) and there are plenty of eateries - the pub at the bottom of the town, The Bear, being the most well known. It will take you about 35 minutes to Woodstock and Oxford is 10 minutes or so on from there.
It may be wise, if you are not used to driving in England and in cities, to park your car at the Park and Ride at Pear Tree Roundabout on the way into Oxford and take a park and ride bus from there which will drop you off in the centre at the beginning of the pedestrianised zone.
There is not much I can say about Oxford that you can't already find in the guide books. For information on Christ Church, probably best ask Tony who read Law there, many moons ago but he won't be able to tell you anything about it as a location for the Harry Potter films as that happened after his time.
The Westgate shopping centre is great! Not only does it have a John Lewis shop but tons of other high street names, all under cover. There are views over Oxford on the top floor which is mostly open and restaurants there are very pleasant in summer time. I think if you get a rainy day at home and you feel like shopping, this would be a perfect place to go.
Just a few pointers of what to see, where to go - places you might like to research further on the internet:
Carfax tower - right in the centre and you can go to the top for a small fee and look over the dreaming spires
See the colleges - 38 of them many prove too many and not all are beautiful - to pick out just two : Christ Church and Christ Church Meadow.
Magdalen College and Magdalen Bridge
Have a drink at the 18th century Turf Tavern. Haunt of TV's Inspector Morse.
New College, where some of the Morse episodes were filmed.
Blackwell's Bookshop, Broad Street. The largest academic and specialist bookshop in the UK. Room after room of Heaven for book lovers.
The Bodleian Library
Ashmolean Museum and lots more museums.
The Botanical gardens
Various walking tours, some of them completely free.
Explore Oxford on one of the hop on hop off bus tours
Punting on the river - take a punt from Cherwell boathouse