Ideas for doable drive for a first night from Dublin

You're making a common but critically important mistake:

You are going to arrive exhausted, in no shape to drive (on any side of any road even in your home town, never mind on the "wrong" side of the road in a foreign country where everything is backwards and "different"). Please don't drive after coming off the plane, it's dangerous. Besides, there's a much, much better and smarter way to go, which is safe, will save you money and you will enjoy it more, too: Don't drive upon arrival at all, on your arrival day. Instead, take the bus right from the airport straight across to the west of Ireland, to Galway. The bus is easy, inexpensive, comfortable (even has wifi, if you manage to remain awake), a no-brainer. It drops you in Galway within walking distance of many accommodations. Walk to your accoms, check in, drop your bag, go out and stretch your legs, get some fresh air, continue to try and stay awake. Have dinner, crash and burn, sleep deeply. Next morning, you will wake up refreshed, feeling So Much Better. Your trip begins that day.

Personally, once in Galway, I'd head out to Inishmor for a couple nights (take the little plane, not the ferry). Upon returning back to Galway from Inishmor, pick up your rental car there, now that you're fully rested, over jetlag, and already feeling Irish. Do your circle route from there. End your trip with a few nights in Dublin - you need to spend your last night there anyway before you fly out, the logistics work much better this way. Basically, circle (most of) the country counter-clockwise, beginning in Galway and ending in Dublin, rather than going clockwise from Cork to Dublin (with a dangerous, uncomfortable drive at the start). This is a great way to begin a trip to Ireland. Please consider it.

Ireland is wonderful - you will love it.

Thanks, David. I truly appreciate your advice. We do want to spend some time in Northern Ireland also so starting Galway (sounds great) but would make going to Northern Ireland an out of the way trip. I see there is a fast train from Dublin to Cork. Perhaps that would work for us. We could take the train to Cork and then stay there before driving, but I'm thinking it may not be as nice as the Galway plan but would allow us to go up the western coast, across the north and down to Dublin. Any thoughts on that plan?

Sure, that could also work. There's nothing magical about going counter-clockwise (Galway then south); you could just as easily do as you suggested, take the train (or a bus, aka a "coach") first to Cork or somewhere in the south, get that first good night's sleep, and after picking up the car there the next day, proceed clockwise. You could continue up the west coast (the best part of the country, IMHO), from Galway continuing north and around into Northern Ireland, before swinging down to end in Dublin.

There are three critical benefits, I think, in using this strategy (CW or CCW direction doesn't matter):

1. You skip the whole (dangerous and not-fun-at-all) 'driving after arriving exhausted' issue.
2. Because flights from the US typically arrive in DUB in the morning, your arrival day is "wasted" to some extent; you can reclaim some use from that blurry day by pushing on immediately after landing, ending the day in someplace distant from Dublin that gives you a better place to actually begin your trip the following morning...but because you use public transportation to get there, it's safe and not demanding (you can fall asleep on the bus or train if you really have to, though for many folks, it's best to tough it out and stay awake until dinner, then sleep very deeply, the next day you wake up and most of the fatigue and jetlag is behind you).
3. You have to spend your last night in (or very close to) Dublin anyway, so spending your first day or two there is logistically inefficient. See Dublin last, instead.

The only specific benefit to starting in Galway (rather than, say, Cork) is that, IF you are going to do a little side-trip out to the Aran Islands (very highly recommended), you do that from Galway, and you leave your car parked there (in Galway), and you're paying for a car you're not using that day(s). If you do that Aran Islands side trip at the start of your trip, you can pick up the rental car after you get back to the mainland, and you're not paying for the rental for the day(s) you are out on the island. It's a minor efficiency, not a deal-breaker to build your trip around.

The Irish rail system is OK (here's a map) but it's not what most Americans think of when they dream of European rail adventures. Trains are perfectly OK, comfortable, etc. but are not sleek, fast TGV-types. It'll get you to Cork in comfort though, and it'll feel good to be out of the plane (when I finished my west coast of Ireland trip, I dropped my car off in Cork and took the train back to Dublin; you would be just doing that in reverse). I did not spend any time in Cork, for us it was just a place that had both a car rental agency (which was open on a Sunday morning) and a railway station (took a taxi between them). Starting in Cork would put you within striking distance of all the great stuff in the southwest.

The southwest of the Republic is spectacular. The entire west coast is very special. I would plan to spend a large chunk of your 3 weeks around the SW, west and NW coasts. Continuing up into Northern Ireland would be great (I saved that for next trip).

May is a bit before peak season, be ready for any mix of weather, you'll probably get a bit of everything.

You'll have a blast.

There was a "should I drive" post a week or so ago, and the "never" vote was unanimous. I've disobeyed that guidance every trip but one, with no ill results. I was a volunteer firefighter for many years and getting up out of REM sleep to go fight a fire or deal with a car wreck was routine. There might be an adrenaline difference, but I'm usually excited to start a tour. This May, I'm planning on driving into the outskirts of Belfast the first day, and the next trip, I expect to drive to Glendalough. My next UK trip will include a drive into Lerwick. Driving from Dubiln to Clonakilty was not something I would do again. I wouldn't recommend it to anyone, but wouldn't vote never.

When we visited I headed north from the airport to Crawfordsburn where we spent the first night. That was a little too far, even for me. I was ready to suggest Trim until your comment. Since you’ll need to go on the M50 around Dublin, I’ll suggest Enniskerry or possibly the Bray area, as far down as Wicklow. Enniskerry is only about a 35 minutes drive from the airport. Wicklow would be 30 minutes further. Only you know you, but for me any drive up to 2-2.5 hours is fine after a long flight. Only you know your capabilities and limitations after a long flight.

You've received a lot of really excellent advice from David, and his comments about driving after a long overnight flight reflect the sentiment of just about everyone here on the forum.
The idea to catch the express bus from the airport to Galway, visiting the Aran Islands first, and then renting the car as you head out of town is a particularly good one. Would save the cost of a couple day's rental - not a minor consideration with current prices for an automatic going for $100 per day.

Malahide. Literally a 15 minute drive from the airport on some very easy suburban roads. Malahide Castle and gardens, seashore, good restaurants, pleasant high street.

Thanks for all the info. It's pretty clear that my first plan wasn't a good one, so I'll rethink with your suggestions in mind. You've all been a big help. Thanks.