Parking: As Paul said, it's expensive. For 4-6 hours in one of the central car parks it's £12 - £14. If you do decide to drive in then I would suggest the Westgate car park. It's one of the (slightly) cheaper ones and is large and, on a Sunday, there should be no problem getting spaces. It's also close to the centre. The train station is close to the centre if anyone considers arriving by train a viable alternative.
To see/Lunch: I think a walk from the Castle through the town centre, passing Carfax Tower (you can climb it if you want), Sheldonian Theatre, Hertford bridge, Radcliffe Camera then out to Magdalen Bridge would give a good flavour of the place. At Magdalen Bridge there's the Botanic Gardens and punting (you won't get me in one). From there you could go further out to Cowley Road / St. Clements where there is a couple of pubs quite close (
The Cape and
Angel) or go further up the Cowley Road which has a lot of different food places. Or could go back towads town along Merton St. and end up at
The Bear. I think finding somewhere to eat might be an issue as it will be busy I'm sure. Might be worth trying to book something.
Just mention another couple of pubs which are en-route if we think doing the above before lunch will be too much:
The Turf Tavern and the
Kings Arms.
Any thoughts?