The newly redeveloped art gallery is the only Welsh institution included on the prize's longlist.
Chair of the judging panel Michael Portillo was joined by three of his three fellow judges on the visit: museums and heritage consultant Kathy Gee, Guardian journalist Charlotte Higgins and Antiques Roadshow expert and curator Lars Tharp.
The four Art Fund Prize judges at Mostyn: Michael Portillo, Kathy Gee, Lars Tharp and Charlotte Higgins. Photo: Martin Lyons
Director of Mostyn, Martin Barlow, told me: "The Art Fund Prize judges' visit seemed to go very well.
"Like the great majority of our visitors they could see that the architecture of the new Mostyn is really quite special, and it was an opportunity to explain just how complicated the transformation was to bring about in the building's very confined footprint and to point out the '4S: Simple, Smart, Sophisticated - with a few Surprises' principle which the design team adopted.
"Equally importantly it was an opportunity to talk about leading Mostyn's role in presenting Welsh and international art and about all the learning activity organised with the exhibitions, and to present the judges with photocopies of the many hundreds of wonderfully appreciative comments left in our comments book by our 70,000 visitors to date!"
The short list of four museums and galleries will be announced on 19 May, while the winner of the £100,000 prize will be awarded on 15 June at a ceremony at Tate Britain in London.
Members of the public can vote for their favourite longlisted museum via an online poll - visit the Art Fund Prize website for further information.