We stayed at the Miller Arms, a pub, which was walking distance from everything and really nice rooms! Canterybury is 2.5 hours away from Cambridge so I think it is too much of a drive in one go so plan to stay here and do a day in Dover too!
There were a lot of pedestrian only zones which was nice.
Canterbury is for Anglicans as Rome is to Catholics. The head (Archbishop) of the Anglican Church is here in Canterbury. This is the Mother Church for Anglican Churches around the world.This church was established by St Augustine.
Canterbury Cathedral was amazing. It is bigger than Ely Cathedral but they are both beautiful. It is said that after Thomas Beckett was murdered in 1170 on the orders of King Henry II, there were miracles that occurred so it made this place popular. I would say that you should expect to spend about 2-3 hours here. There is an "American Trail" pamphlet that guides you to items that are of particular interest for Americans such as the monument to Thomas Peircy who is credited to inventing the US Navy.
If you are a freemason, you might like to visit the Kent Museum of Freemasonry
You can also visit the Norman Castle.
I really loved the charm this city had, its amenities and everything about it really.
All the Best!
American to Britain