Like some posters have already said, looking at the title I thought this thread was about the two ancient universities. Now I see you have no preference living in either of these two cities but it's only the two preps that will eventually decide where you'd live eventually. When I see 'Dragon' I said to myself, Oh Lord, NO!
You want any school but Dragon, OP. Oxford is a very nice place to live - I've lived there for three years but have only visited Cambridge a few times. I know absolutely nothing about St John's. Based on my experience on Dragon, I'd say Cambridge and St John's is your answer.
But if you must live in Oxford, the prep to go for is Summer Fields, just a short distance north of Dragon.
Why the hatred for Dragon, I hear you ask? For a start, they were totally disorganised - sending my correspondence to another family with the same surname half a world away. And when we visited, they spent more time telling me which big wigs had gone there or had DC attending there instead of telling/showing me more about the school.
Finally, the last nail that went into their coffin was when they asked me for the 4th or 5th time how was I going to pay the fees. If they had known better, fees would be the very last thing they should worry about and in our case should be the absolute cast iron safetest bet that they would be paid. If anything else, just shows you how ignorant they are!