I studied in Canterbury once upon a time. Not there any more, but of you're interested in routes-
Have a look at Blean woods (nature reserve?) for graveley stuff and xc.
There's a pleasant gravel cycle track goes from Whitstable to Canterbury through some woods with lots of gentle off-roady stuff going off it.
There's a nice circular national cycle route going from Canterbury to Dover and back, about 50 miles on road.
And many, many country lanes to explore.