I visited Canterbury in August 2015, beginning with a drink outside Christ Church Gate to the is mixed Romanesque and Gothic cathedral that is the seat of the most senior figure in the Church of England.
The crypt held quite a surprise for me, as I was not expecting to see twelfth century frescoes in a C of E cathedral. The paintings, located in St Gabriel’s Chapel, were painted long before the C of E was created under Henry VIII, and the chapel was bricked up soon after its creation. It was discovered in the late nineteenth century, with restoration work finishing only in the 1990s. The frescoes put me in mind of the crypt at the Basilica of Aquileia.
St Augustine’s Abbey is a ruin, wrecked by Henry VIII in the Dissolution of the Monasteries. I didn't find it greatly interesting, I'm afraid.
St Martin’s Church, a ten minute walk up the road from the abbey, is an unassuming little building that looks like any other English parish church. It dates back to slightly before the abbey – so old, in fact, that Roman bricks have been found to form part of its structure. It is the only free-to-enter site of the three, and is a charming oasis of calm that is overlooked by most tourists to the city.