Whichever means of transport you choose to get around Oxford, it can be a nuisance. Going by car is by far the worst option as there is hardly any affordable parking in the centre (and similarly further out). Moreover, the centre cannot be traversed during the day - the only road that leads through it is reserved for buses and taxis, and even they can't go the whole way through as a pedestrian zone blocks the way.
Going by bike is, as mentioned elsewhere on my pages, rather dangerous as there seems to be a general hostility towards cyclists. Many cyclists, however, do their best to fuel this hatred by going without lights at night, ignoring red traffic lights and zigzagging through the densest traffic only to be a few seconds faster. In 2011, 58 cyclists were killed or seriously injured in Oxford - and while it's easy to search guilt among the reckless car drivers of which Oxford has thousands, there are more than enough cyclists who take risks they don't need to take.
Going by bus looks like a safe and reliable strategy, but it's only worth it if you take a week ticket or so as a single ticket costs approximately £2 per kilometre! Moreover, more often than not there are 3 buses of the same line coming at once, and afterwards not a single one for 20 minutes. At least the bus companies have now introduced a scheme that allows you to take buses of different companies with the same ticket - i.e. unless you buy it on the bus. Don't ask me why, but they seem to want to complicate everything as much as possible.
That leaves walking, which, if you are a good walker, is indeed the best way to get around in Oxford. Most of the sights are within 15 minutes walking distance from Carfax Tower, and those that are not normally include a nice walk along the Thames or the Cherwell. Be aware of reckless cyclists, though...
I find the best thing to do to avoid the traffic and parking nightmares when visiting Oxford City centre is to use the Park and Ride facilities. There are 5 sites around Oxford; Thornhill, Seacourt, Redbridge, Water Eaton and Pear Tree details of which can be found at ParkandRide.net The National Park and Ride Directory. This is also a green, environmentally friendly way to visit the city centre.
Traffic in Oxford can be occasionally chaotic - i.e., every morning and evening at rush-hour. On Saturday nights it can be very difficult to get parking in town. Oxford is fairly small and compact, and the best way to see it is on foot!