With isotopes, is it fair to say that each isotope has a slightly differnent volume due to the differing numbers of neutrons in the nucleus? i.e. carbon-12 is slightly smaller in volume than carbon-13. If not, why?

The volume of a nucleus has little impact on the volume of the atom. It is akin to saying the size of a football field is dictated by the size of a pebble found near the fifty yard line.