Soren,
I did a similar trip recently (Ballybunion Old 2x, Lahinch 2x, Tralee, Doonbeg). First - you will have an amazing time no matter how your itinerary shapes up. It was an amazing experience.
As to the golf, Lahinch was my favorite (and that was consensus among my group). Just an amazing mix of interesting and fun golf holes. Just to warn you, don't be surprised if you are practically ignored by the starter before you tee off. Once you get out on the course it's all good. I would also recommend checking out the Cliffs of Moher while you are there.
Ballybunion was a close 2nd though. Just FYI, the greens are new there so very slow currently. I really liked our hotel across the street from the course (Teach de Broc). I would definitely recommend playing BB and Lahinch 2x if you can. I did not play the Cashen course at BB since I heard mixed things, though I would probably give that a go next time.
I would put Tralee a notch down below those two, but it's still worth a play. The front nine is fairly open, while the back is quite dramatic, playing up through the dunes. Not as pure as BB or Lahinch, but still a cool place.
Doonbeg would be my last of the ones we played. It's worth a play if you have time, but your life is quite complete if you don't. Feels more American than the others - pristine but less interesting. That said, there are some good holes and nice views.
I did not make it down to Dooks, Waterville or Old Head. Next time!
Kevin
PS - don't ditch the rain gear if it's sunny when you tee off. It can go from sunny to heavy rain/wind to sunny again in an hour.