I confess that I've looked at the answers to this question for a lot of European countries by now, preparing a number of these posts. There aren't many where the top book is as far ahead of the field - on both LibraryThing and Goodreads - as it is in this case. And there are even fewer cases where it's a book I simply hadn't heard of. But this is one of them. The most widely owned book by a long way (among both LibraryThing and Goodreads users) which is set in Wales is:
Miss Peregrine's Home for Peculiar Children by Ransom Riggs
Apparently it's a beautifully illustrated and spooky book for YA readers, published in 2011. It's also the most frequently tagged "Wales" by Goodreads users, and third on LibraryThing.
The two books most frequently tagged as "Wales" by LibraryThing users are:
The Mabinogion (Librarything)
Here be Dragons by Sharon Kay Penman (Goodreads, second on LibraryThing)
I am of course familiar with the first of these. The second is the opening novel of a historical fiction trilogy, which has clearly done well while passing me by.
Fourth place in LibraryThing tags, and second on Goodreads tags, is the one I would have immediately thought of:
How Green Was My Valley by Richard Llewellyn
Bubbling under, Fall of Giants by Ken Follett (second most popular "Wales"-tagged book on Goodreads), The Grey King and Silver on the Tree by Susan Cooper, Among Others by Jo Walton, The Chronicles of Prydain by Lloyd Alexander - not all of which are entirely or exactly set in Wales.
Sorry, Dylan Thomas. You didn't quite make it to the top. (Nor did Torchwood.)