Ireland is a hotbed for the horses for various reasons and a visit to a meeting is an excellent alternative attraction. There are four racing courses quite near to Dublin - Leopardstown (south country Dublin), Fairyhouse (Co. Meath but near the Dublin boundary), Punchestown (Co. Kildare, not far from Blessington and Naas) and the Curragh (also Co. Kildare). The best-known Dublin course is Leopardstown where the most famous meet is held on Easter Monday (many Dubs were there in 1916 on the day of the Easter Rising). There is easy access from the city centre and it's only about six miles away by bus, car or taxi. The Curragh hold the Irish Derby in mid-late June and always features a great mix of racing, style and craic.
There are two types of racing in Ireland, flat and national hunt (jump racing or hurdles). The curragh in nearby Co. Kildare is the home of flat racing and the season runs from March to November.
National hunt happens all year with the main focus from November to the end of April, celebrated by the Punchestown festival. Fairyhouse festival happens over the Easter holidays and makes a trip to Ireland well worthwhile during this time. With the recent abolition of betting tax, you might even consider a 'flutter' on the nags!
For more information on horse racing in Ireland, try the Irish Horseracing Authority's website. If you wish to buy a horse, Irish Thoroughbred Marketing can offer excellent, impartial advice.