It's worth taking the train to Hereford. The train takes a couple of hours but it's a beautiful journey, you pass through some fine countryside, and end up at a fascinating town that has much to offer for the day: an ancient cathedral, lots of shops, a gorgeous river. And all for the price of a train fare.

London is an accessible day trip from Oxford. The train takes one hour, and the bus (a much cheaper option) takes about 1 1/2 - 2  hours.

Bicester Village Shopping Outlets can be reached by buses #27 and X5 from Oxford's city centre. 

Blenheim Palace (open mid February - early December) can be reached by taking the #20 bus from the city centre.