I don't sell shamrocks, but I spent a summer in England/Ireland once. The western side of the island is starkly beautiful. Bicycled around the west coast of Ireland from Cork City up to the North. The winters, well, the gulf stream will keep Galway Bay warmer than it would otherwise be, but its still going to be winter. Still, I'd retire there if they'd have me.
There is Celtic history and artifacts, to be sure, but obviously much of the written history will be from after the time of Patrick.
Some the more touristy things we saw that I'd recommend are (in no particular order): Ring of Kerry, Gap of Dunloe, Poulnabrone Dolmen, Cliffs of Moher, Aran Islands (and Doolin!!!), Dingle, Ross Castle, even Croagh Patrick if you are so inclined. If you get to the North: Giant's Causeway. Every town, village and hamlet has several pubs (though some will only be open in the summer), do your best to spend your evenings there or wherever you hear music wafting out.
I'll stand aside and let the expert give you more useful information.