Brad
Spangles is right. RCD to Portrush to Ballybunion is too much windshield time for ten days - really only 8 days with two half days. There is plenty of good golf - no need to run around like a chicken with its head cut off.
Assuming you are flying into Belfast and out of Shannon and it is your first time playing any of the courses (still a bit of a busy trip for my liking - I would stick to 1/2 areas, but here goes):
1. 18 Portrush Valley - off the plane
2. 18 Portrush Dunluce (can play 36)
3. 18 Portstewart (can play 36)
Stay at
http://www.adelphiportrush.com/ for the first three nights. Be sure to try the oriental part of
http://www.ramorerestaurant.com/4. 18 Portsalon (can try to slip in Cruit Island between here and #5)
5. 18 Narin & Portnoo
6. 18 Donegal
7. 18 Enniscrone (can play 36 - Strandhill just outside of Sligo is charming)
8. 18 Co Sligo
Stay in Sligo for #s 6, 7 & 8 - there are a few chain hotels in heart of a reasonably attractive town.
9. 18 Lahinch
10. 18 Lahinch
I would definitely skip RCD as it fits much better with a trip to Dublin working north with Baltray. It is way out of the way for what you are doing. You will be seeing plenty of greatness -don't worry.
I would consider adding Ballybunion, but its well out of the way (Lahinch is perfectly suited to finish at - 45 minutes from Shannon). It depends on if you don't mind skipping Narin & Portnoo and Portsalon. Then you could add two days for Ballybunion, but see less. Again, a trip back to Lahinch, Doonbeg, Tralee etc gives another chance to do Ballybunion properly.
It is a shame to miss Carne, but it is out of the way and can be picked up easily if you ever go back to the Donegal/Sligo/Enniscrone part of the world - and you should.
Ciao