You can wander into the town centre of Strood but obviously you will not seem any remnants of horse atrocities in the town. If you want to look at Medieval then you could go the nearby Temple Manor the land upon which it sits was given to the Templars by Henry II in 1159. Although the actual Hall you can now see was constructed after Becket’s death. If you want to see some sights that Thomas would have gazed upon then you can head over to Rochester Castle and Cathedral.
If you are looking for refreshments in Strood then might I suggest the 10:50 from Victoria which is a cracking micro pub. You might even be able to try some Longtail Cider which is brewed near Strood and takes it’s inspiration from this very story.
If you have enjoyed this tale of Thomas Becket and his beef with the people of Strood, perhaps you would like to read more on the subject then here are some academic works I perused.
A Mediaeval Slander by Lilian M. C. Randall in The Art Bulletin Vol. 42, No. 1 from 1960.
"Tails" of Masculinity: Knights, Clerics, and the Mutilation of Horses in Medieval England Author(s): Andrew G. Miller in Speculum, Vol. 88, No. 4 2013
Mysterious Britain website on Kentish Longtails
The really excellent blog called A Clerk of Oxford.