Greetings from Ireland.
Sounds like your trip will be a lot of fun. To play golf with locals and join them in 19th hole afterwards for a beer, you might want to avoid the big expensive and famous courses. I find the courses in royal Portrush, the K club and Trumps place in Doonbeg a bit like being on Wall Street, there are invariably loads of rich male American bankers playing, Irish people too of course but often the majority are rich Americans. Nothing wrong with that of course, but you did state you want to play with locals.
There are tons of great courses in Dublin, my uncles are members, and its a very authentic, accessible and affordable golf experience. As is the local course near me in Dingle, as are hundreds of others.
Im not sure what you mean by saying in places that are 'euro-centric'? But if you want authentic local experiences, they are to be found in abundance. Be careful not to rule out places like Dingle, Galway or Westport, that get a lot of tourists and some people in this forum will say avoid, because of the amount of tourists. These towns are where I find the most genuine local fun experiences anywhere in Ireland, and I have traveled around this Island as a tour-guide for 20 years, so Im talking from experiences.
Enjoy the golf and don't have too many 'Ryanair shots', y'know were the ball flies well in the air but doesnt land where you want it to.
Le meas/with respect
Rick Steves Ireland tour-guide
Dingle & Derry