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 - N
The 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!!!