What are the chances, in early to mid-September, of being able to fly in to Dublin, spend a night there, and then head west for, say ten days, finding a place to stay wherever our travels happen to take us (2 to 4 people)? In other words, is it possible to have accommodation reservations for only the first and last night and freewheel it in between, like you pretty much can in the US after Labor Day? Thinking mostly of the west coast: Galway, Connemara, Mayo, Donegal, maybe a jaunt into N. Ireland. Looking more to experience Ireland and the Irish than to see touristy sights. Never been to Ireland before, so I have no idea what to expect, other than what I learn from guide books and forums like this.
It's been years since I did it, but I still believe that a car should make this feasible. If you can decide and book lodging a day or two ahead along the way, even better. Of course, two people will fit into more availabilities than will four people. Remember that being flexible means being willing to take what you find, including moving on to check the next town, instead of getting what you want when you want it.
We spent last August traveling around Ireland and never had a problem with finding accommodations. We did book a couple of days in advance, though.
I never book anything in advance, and I always find plenty of places to stay. September is shoulder season. You shouldn't have any problem.
In nine trips all over Ireland and Northern Ireland since 1988 (all in the height of summer and early fall), we had a problem securing B&B accommodations - right away, that is - on just one occasion. And that was in a popular commercial town (Westport, County Mayo) on a Saturday evening in the summertime. Even then, we found rooms in less than an hour. On every trip, we just called ahead during the day or knocked on a door or two once we arrived in town. And we were bicycling, not driving.
You're wise to make reservations for your first and last nights, as we always do. Keep in mind, though, that with four people you may or may not find rooms at the same facility since B&Bs have fewer rooms than do hotels.
So, freewheel it to your heart's content and enjoy the travels - no matter the time of year. Ireland's a small, exceptionally friendly country with over 2,000 B&Bs, as well as numerous hotels, from which to choose.