I know it's not particularly near Llanwrwst but the Bridge Cafe in Blaenau Ffestiniog needs further recognition.
It seems a regular kind of cafe on the surface but go downstairs and it turns into a shrine of caving (ok I know caving isn't mining but let's not split hairs....).
There is an informative display on the history of caving, interactive computer thingies and even speaking caver models. Pride of place is a proper cave experience with stalactites and passages and a properly engineered squeeze box for the really keen.
Gaile the owner deserves the OBE equivalent in the caving world for services to the underground - and she told me she had never been underground in her life!
Oh and she does Olympic Breakfasts!