I'm mostly steering clear of natural sites as I don't have much knowledge, but I do have a little to draw on for volcanoes. Below is my list drawing a fair bit from Colvin's reasoning:
Giant's Causeway -
N/Y Interesting but is it more of a quirk than representative of volcanism? I ask that as a genuine question if anyone knows.
Hawaii Volcanoes -
Y Agree with Colvin probably the best example of volcanic island building.
Heard and McDonald Islands -
N? I don't know enough of it's relevance, isn't the main focus on it's remote nature and thus untouched flora and fauna rather than Volcanic activity?
Hierapolis-Pamukkale -
N Quirky but examples at Yellowstone would perhaps be better
Isole Eolie -
Y Interesting variety of examples, and also instrumental in the scientific study
Jeju -
N/Y A bit like Giant's Causeway, interesting and quirky but not sure of its merits beyond that, but again I don't know much and am open to further explanations.
Macquarie Island -
N? Again like Heard, is it more of relevance for it's Flora and Fauna than volcanism
Mount Etna -
N/Y Seems the definitive Volcano, but perhaps active volcanism is better covered by Hawaii, and Startovolcano by Teide? Also I have a feeling Italy will have a lot of things on the list anyway.
Pitons Management Area -
Y/N One of either this one or Reunion seem like good examples for volcanic plugs, I don't know which is the better example
Pitons of Reunion -
N/Y One of either this one or St Lucia seem like good examples for volcanic plugs, I don't know which is the better example.
Surtsey -
N Great to have a site studied from it's very creation, but perhaps Hawaii is a better example of Island Building
Teide National Park -
Y Best example of a Startovolcano?
Ujung Kulon National Park -
NThe focus is more on the Flora and Fauna rather than the Volcanic activity
Volcanoes of Kamchatka -
Y Best inscribed site from the Ring of Fire, also it just looks brilliant.
Yellowstone -
Y Could say about all the exceptional geothermal features which would be better examples than other in the list, but also could just say:
SUPERVOLCANO!!!