Oxford, famous for its University, is full of beautiful old buildings. It's a small city and very easy to get to via bus from Bicester. It's worth a little day trip out.
If you are a Tolkien or Lewis fan, then you should check out this pub in Oxford - it's where the Inklings would meet to discuss their writings.
Ethan loved visiting Blenheim when he visited England. Once home to Winston Churchill, and set in the idyllic English village of Woodstock, there are plenty of walks to go on, and pubs to stop at on the way. About 25 minutes from Bicester, you will need to drive, or you can take a bus from Oxford :)
While, in England, you really should take a day to go and see London! Full of all the famous sites, good restaurants, and fun activities, it makes for a great day trip. It's my favourite city. You can catch a train from either "Bicester North" or "Bicester Village" and both will take you directly to London- you are only 50 minutes away from the big city!