Excellent report! I don't know if it's currently on display, but they used to have an original drummer's coat from the latter half of the Napoleonic Wars belonging to the Royal Carmarthenshire Fuzileers Militia. Most unusual, as it was in the 'reversed colours' of blue with red facings, when the regulations stipulated that blue facings should not be reversed.
I am somewhat disappointed though, that your visit didn't take you to either the City Arms, the Goat Major or the Cambrian Tap...
