This map locates the following towns:
- Bedchester, Binchester, Chesterblade, Chesterfield, Dorchester, Ilchester, Manchester, Porchester, Portchester, Silchester
The suffix -chester comes from the Latin castrum meaning encampment, and is the Anglo-Saxon version of the word. Old Norse, however, did not have an equivalent of ch, and so places might have suffixes suuch as -caster, -caister, -cester: see The History of Early English, K Johnson, Routledge, 2016. You can make questions harder by including a selection of these other versions. This map may help:
Just where the Romans pitched their tents is pretty clear, here, I think.Geeks might like to note that Exeter is derived from the Old English Escanceaster and so arguably counts, although Wroxeter and Uttoxeter do not. This topic is considered elsewhere. There are no other -xeter's.
Nota bene: this post would have been very difficult without access to the Gazetteer of British Place Names