Their isn't much about eating establishments in the travel book, but the Erskine Arms in Conwy is a must. It is just across the street from the Train Station. My sister, brother-in-law and I ate there three times. A local favorite.
Another fun pub is the Liverpool Arms on the waterfront. Not for meals though.
"Conwy, Wales, England?"
Ahem. Don't think the Welsh would be very happy about you locating Wales in England... ;-)
There actually used to be a pub in Llanymynech that was in both England and Wales as the border cut through it. The bar in Wales had shorter opening hours than the two in England because of different licensing laws.