Rebecca, Welcome to the forum. How you plan your itinerary will depend on what you plan on seeing each day. Some places are perfect for day trips, others are not. Do you have a "must see" list to add to your itinerary?
Generally, I find that most people who visit Ireland for the first time try to do too much. If you can stay in a couple of strategic places for two nights it usually makes for a better trip.
When you have limited time another tip is to save Dublin for your last two nights instead of breaking it up into first and last. That way you can get a jump start on your trip. But it also depends on your arrival time. If arriving late in the day then you will want an overnight in Dublin. If you arrive at 8 am then maybe consider up to a two-hour drive if you feel competent to do so.
One place to spend more than one night is the SW. Killarney or Kenmare are perfect for that.
We will be there June 3-11, 2015. I'm reading more threads and am thinking maybe we should fly into Shannon instead and just stick to the west coast? I probably am being too ambitious... This is probably a once in a lifetime trip for us, so I want to see as much as possible. There's nothing on our must see list though, except for some cliffs and a few castles. I would like to stop in to a few small villages... Other than that, I just want to look!
If you are not that interested in big-city life then I highly recommend you fly into and out of Shannon. It is a great little airport and you will not have to contend with Dublin traffic. There is plenty to see and do that will totally fill up your time in the west and SW.
Rebecca, you will definitely have a much easier time of it just flying into and out of Shannon. It is massively easier to drive in and out of that airport compared to Dublin and I can promise you that you won't feel short changed or that you missed something if you stick just to the west coast. There is so much to do and see there and even in 8 days you will have just scratched the surface.
You might consider just cutting down your itinerary to just the counties Galway, Clare, and Kerry and stay in one place in each county. This will cut way down on the headache of checking out/checking in/finding your hotel/packing/unpacking each day and give you more time to get out and to day trips in each county and more time to sight see and do the actual stuff that you want to do. Less is more and in those three counties there are plenty of cliffs, castles, small villages, and phenomenal pubs to visit to keep you plenty busy for 8 days.
have to second what markan said, did you know Ireland is a once in a lifetime experience as you say, that many return for. I would say Base yourself in Killarney and Somewhere in Clare and keep it simple accommodationwise. No matter where you go in ireland you will be spoilt for choice. The more you read online the more you will want to do.
What do you enjoy doing mostly, and organise around this.
Lively nightlife?
Walk on Beach?
Hiking?
Irish Music?
Golf?
etc....