Thanks to Roger for the picture and information:
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The present Royal Hotel is not the building that the Banks family built. As you can see the building they built is closer to the seawall than the Royal is today. I'm sure this one was called Kent House and was the place that Banks proposed to build a pier off the seawall. The Trinity Church is comparatively new although there are a few gravestones in the area. Trinity road was still unsurfaced but there's that clock in the foreground. It was moved to the Quadrangle in the dockyard, I've seen a picture since showing that.
Oh yes and this one was taken before the Conservative Club was built.