Are you visiting with the intention of checking it out for one of your children? Or for tourism?
If for a prospective student child, I'd look at their intended academic area and then compare departments at the schools.
If tourism, go to Oxford! Alice Liddell lived there; her dad worked at Oxford, and Lewis Carroll also lived there (he was a don). The story of the "real" Alice will fascinate you, and you can read Carroll's book to your kids on the way over, or show the movie. Then, you can take the Alice city/Oxford tour when you get there. This involves a walking tour of where she and Lewis really lived: I loved seeing the real gate in the hedge that is supposedly Carroll's inspiration for the rabbit hole/White Rabbit. And you can go to Alice's Shop, which used to be the real sweet shop where the real Alice went, but is now an Alice themed gift shop (if you have daughters, you can get them the adorable dolls). Plus, Shakespeare's home town is a day trip from Oxford.