Where in Ireland for racing?

Did you see that someone just chose as the best answer as to where they would most like to fly would be Ireland? Helluva good choice. I've got a story or two about traveling in Ireland in 1969, after I got out of the American military but this is not the place. My question is, I love horse racing and have often thought that I would like to go to Ireland and visit several different courses. What would be a good time of the year to go and where would be a good place to start? Oh, FYI I'm American so I speak a version of English but i do understand a bit of Irish, but not Gaelic