Hi,
What part of Ireland are you planning to visit? To be honest I do not think you will find a bad course and the welcome is always fantastic. I haven't been for a few years but my last visit took me to the two Druids courses (Glen and Heath) and the European. The European is simply stunning and quirky.
There was (there may be now) no pro shop or club house to speak off, no fancy tee markers, it really was just a course carved out of the land and left to its own devices. Well worth a visit if you are going that way.

I can't recommend The European Club highly enough, an absolute masterpiece. Don't expect a luxurious clubhouse, do expect one of the best and toughest courses you'll ever play.

Those lists are pretty good from experience in the UK, and all the usual suspects are up there!
I haven’t played golf in Southern Ireland but I’ve played in NI and can wholeheartedly recommend Royal County Down, probably the best course I’ve ever played.

Well I live in Ireland if you wanted to adk me I’d be happy to help. What part of Ireland are you going to spend Most of your time in?
Are you looking for links style golf or parkland?
Are you looking to play high end golf like say old head portmarnock royal county Down or something a little more relaxed?

What type of course are you looking to play and what time of year?

I'm a little biased as my father is from Ballybunion and a member there (as a number of uncles and cousins!) so I've played there a lot over my golfing life! I love it, the Old Course is fantastic as is the Cashen Course.

I also have uncles who are members at Tralee and Killarney. Both are great courses.

I've played a number of other courses around Ireland, Waterville, Carton House, Fota Island etc. Back in April I played up in the North for the first time at Royal County Down and Royal Portrush. County Down was one of the best courses I have played, but for me, Portrush didn't live up to the hype. Not sure why, its a great course, but I expect a little more wow or something.

Just having a look at the link and its reminded me of some others I've played over the years....

Carne, Portumna, Esker Hills, Castlemartyr.

I also dug out this link to the conditions myself and some friends played in back in October 2014 at Killarney.

www.youtube.com/watch

We sailed over Thursday, played Fota Island on Friday, it was a cold damp start and we got a good bit of rain on the course. Ballyb Old and Cashen on Saturday, beautiful blue sky, wind was up and cold. Warmed up so we removed some layers then the heavens opened for a few holes! Killarney was a very wet day, (check the link!!) we stayed out there because we were already soaked through and it was quite good fun! Then at Tralee on Monday we again had beautiful blue skies, shortly followed by a hail / sleet shower and then warming up to blue skies again!! One of the lads who came with us had never been to Ireland and didn't believe us that you could get all 4 seasons in a day!

For Ulster golf I'd say that both Royal's are a must (Portrush & Co Down). I'd also recommend Portstewart where the Irish Open was this year and also Ballyliffen (play both courses) where the 2018 event is being held.

Would also recommend Rosapenna in Donegal as well.

All of these are great links courses but there are many many other very good courses too - Castlerock, Ardglass, Portsalon (the list is endless).

Dont for get your waterproofs! It's not called the Emerald Isle for nothing :-)