I have been to Dublin, Cork, Edinburgh and Normandy, but not Liverpool, Belfast, Invergordon (though I have been to Inverness) or Guernsey. I lived in London for three years (which is why I've been to most of the above places).

In Dublin, there's a pretty walkable area in the center of the city on the south side of the Liffey. I really like walking on the Trinity College grounds, and though I haven't done it, you could go see the Book of Kells (look it up). From there take Grafton St. (pedestrian shopping street) to St. Stephen's Green (big park with a pond). From there go west toward St. James Gate (Guinness brewery tour). St. Patrick's Cathedral and Dublin castle are in-between, depending on the route. And of course there are a zillion pubs, and you have to have a Guinness at at least one.

Cork is inland, though the River Lee runs from the south all the way into the city. I'd be interested in where you actually dock. I don't know the city particularly well, but I do know you order Murphy's, not Guinness.

In Edinburgh, the castle is pretty much obligatory. The area around it, however, is super touristy. The Palace of Holyroodhouse and Holyrood Park are a bit less busy and also pretty cool. I'd say take a day trip but not sure you'll have much chance.

From Invergordon it's probably worth going down to Loch Ness. Yeah, it's just a lake. But it's actually quite beautiful, as is much of Scotland, and if you're going to see one lake, it might as well be Loch Ness. Urquhart Castle on the western bank is cool, and worth a visit. The route from Invergordon likely takes you through Inverness, so you can stop on one way or the other and poke around.

In Normandy, the beaches are great, but you HAVE to go to the American Cemetery. Simply one of the most impactful places I've ever been. I'd check out St. Mere-Eglise, and the church, if you have time (and especially if you watched Band of Brothers).

London requires a whole other post. If this is helpful, I can try to send you more thoughts later this week.