I really should work out a way to get to the Holy Ground to meander (if one can do so on two wheels) among standing stones & tall tales. 
The main roads here are heavily populated by fast traffic, dangerous for cyclists. But if you want to spend the time, you can plot a course on the lesser roads and jumped-up farm roads, "meandering" along from standing standing stones to standing stones, with Tara, the Druid's master clock like the atomic clock is the reference today, as the high point. The standing stones are all marked on the local scale Survey Maps, complete with their own symbol, though it'll cost you a bit in maps and weight and space; you could look at putting them on your phone. Or whatever you like as a focus; for instance we spent several days in the Burren, an area of alien mien and behavior, something like that area in the Namib Desert which blooms overnight for a week every year from horizon to horizon, and then overnight is just blank sand again as the tiny succulents feeding on the dew that blows in from the Agulhas Stream nearby fold themselves into the sand for another year; my mother, who otherwise hated camping, would camp in that forbidding desert for three weeks to be certain of catching few days of beauty. Many cyclists speak enthusiastically about the Wild Atlantic Way, which in return for some discomfort from the wind off the ever-present Atlantic, or a lot if you chose your time wrong, is a very beautiful ride, even if not as informative for the curious cyclist.
Note that there's a series of hillwalkers' paths all over the country, theoretically permitting walkers to circumambulate the island, and many of them are passable on a bike, though some stretches might be hard work, and at others you need local knowledge to stay clear, find another way (I have in mind one where the Lee River -- the mighty river that divides into two around the central island of Cork, just Manhattan without its Central Park -- is shown but it's actually a fingerling stream you can step over, but just of out sight from there, the path ends at a cliff, which is dangerous enough to descend, never mind carry a bike down, and anyway, the rock face ends directly into a pretty large lake, which froze us as we swam across, and ruined our food and my dry shirt in one of the ladies' backpacks -- we discovered later that before the path to the origin of the "mighty River Lee" we should have walked along a tarmac lane for about twenty paces, and taken another, later version of the path which would have taken us around the downslope of the cliff and around the forbidding lake below). When he passed away, my chum Philip and I were planning a ride on one of these paths that has been tarmacced for about 40 miles near Rosslare, which is also the port at which the ferries from Pembroke, Fishguard, Roscoff, Cherbourg and Bilboa dock. There are also ferries directly to Cork (not very well served, perhaps because the crossing is inevitably a bit rougher than the others), Dublin and Belfast from the Continent and from the UK.
One day I came out of the library and found another cyclist waiting by my bike. Out of the airport his carbon seat post had broken off and stabbed him in a tender place. I took him home with me and after inspecting his wound, took him straight down to the surgery, over which in those days I lived, to be stitched up. He was a Scottish doctor retired young, very fit indeed. Because of the cheap air tickets he bought, he was taking only two days to ride first south from Cork Airport and around the Ring of Kerry and from there straight up to Belfast to make his return plane. Crazy doesn't begin to describe it; it's very likely on the stupid side of two hundred stressful miles a day, not worth even plotting on a map for any cyclist with his mind in gear; you'll miss everything good along the way, and to make his plane he'd have to go on main roads up the spine of the country. He had literally no luggage except his toothbrush and his credit card, and a rain jacket so light it rolled up into a tiny tool case. He'd stayed in Irish guest houses before and knew he could count on the landladies to wash and dry his gear. He wrote to me later that he made his plane with time to spare.
That's perhaps the sort of tour you want to make in featureless place, but that doesn't describe Ireland (except on the main drags, where ulcers are born), where the small details -- and graces -- matter. Gee, mom, I missed riding through the Gap of Dunloe (if you go there, remind me to tell you the tragic story of those small squares marked out by stones exactly as I once told it to an Israeli Cabinet Minister who was an old economics teacher of mine, returning his many favors), kissing the Blarney Stone, and Bunratty Castle, and Yeats' Tower, and the Cliffs of Moher, etc, etc. When seen your fill of standing stones, all of these and much more are accessible without over-reliance on main roads, but only for relaxed and unhurried cyclists. I think nothing of making a four-day tour that takes me no further than about 60m from home as the crow flies and maybe two or three times that in total miles out and back, leaving plenty of time to visit features the landladies identify for me, and stopping to draw or paint what takes my fancy.
Note that if a main road is unavoidable and you don't like the looks of it, that the country buses will let you put your bike in the luggage compartment. This is at the driver's discretion, and if there's space in the luggage compartment, but my bike has never been refused, though I take care not to demand the service on Friday afternoons or Monday mornings in the same direction as the multitudinous students are traveling. There's also supposed to be a fixed fee for the bike, same whatever the distance, but, again, I've never been charged. There are also mainline trains between the major cities on which you're supposed to put your hefty luggage in the luggage van, presumably including your bike, but I don't use them as they just drop you inconveniently in the middle of another city. But Cork Train Station is the exception, a three minute ride from the Cork Bus Station, where you can take bus to the other side of the city, beyond the high-speed bypasses with their inconvenient and dangerous roundabouts (there are no pedestrian crossings), and then start pedaling east- or southwards. Both the train and the bus stations are the same three minutes from the famous hostel behind Isaac's Restaurant, or you can turn the other way from the station and start traveling north- or westwards without the hassle of crossing the city centre, and be in the countryside in ten minutes. Well, you might first have pedal or push over a hill that the professional cyclists on the Tour of Ireland purely hated.
***
About your surname, John, I'm no expert on Old or Middle English, or Alte Deutch, but there are other possibilities, of which armourer suggests itself to me. All those languages, from their earliest incarnation, were portmanteau formers (something English, itself a Teutonic language, has largely lost), so I imagine that you will need to find at least two and possibly more contemporary words, with elisions at the joint(s), to be reasonably certain of the derivation at the time your family name arose. But the first time I heard your name, I thought Axe Wielder, that tall guy right next to the Pike Man. BTW, your actual Teutons, the ones who won the psychological war by winning Augustus' Eagles (the standards of the two defeated legions), only later copied that short stabbing sword from the Romans; their weapons in the time of Augustus were short-handled axes and short stabbing spears, much like the Zulu stabbing spear, very suitable for close-coupled forest fighting where the Roman spiked shield and sword were an awkward encumbrance in the underbrush of unmanaged forests.
***
Thanks for the reference to those books; I'm off to order them. FarFarers is a typical portmanteau word!
