Late spring and early autumn are the best times to visit Canterbury — May to mid-June and September into early October. The weather is reliable enough for the river walks and pub gardens to come into their own, the long English afternoons let you do the cathedral, abbey, and a punt in one day, and the worst of the school-holiday crowds at the cathedral have either not arrived or have gone home.
July and August are not unpleasant but the cathedral and the High Street can feel crowded; the school crowd arrives in coach loads. Winter has the advantage of empty pews — visiting the cathedral on a cold weekday morning, with the choir rehearsing Evensong, is the closest you can get to how a medieval pilgrim would have seen the place. The Christmas markets in early December are charming and not yet too commercial.
For events, the Canterbury Festival in October is the main cultural week of the year — music, theatre, lectures across multiple venues. The Medieval Pageant in summer is part-procession, part-historical re-enactment, and unselfconsciously enjoyable.