We'll be leaving Sligo(after 3 day wedding event) on Jan 1. Have never been to Ireland. Have a 4PM flight back to NYC on Jan 4, out of Dublin. Will have a car(rented from Atlas Rentals. Have looked at endless possibile itineraries. Would like to see as much as possible and have a varied experience. Am open to stay in 5* hotels.
Where should we go? What should we do?

Is there a reason you want to go to Kenmare after Sligo? It's a great town, but a very long drive. (Close to 6 hours, I'd guess.)You might consider exploring in Galway or Clare before heading to Dublin.

I agree with MaryZ Clare would be your best bet IMO.
The Burren and surrounding area has enough to keep you busy for three days easy. dont stick to the main roads ,yes you will travel faster...but you will miss alot. Ireland is at its best away from the main roads.
Northern Ireland( Belfast,Anterim Coast) would be another option.

Mary is absolutuely correct. Too much driving. The sunrise is just before 9:00 and sets at about 4:20, so you have limited daylight. You won't have a lot of time for tourist like things and many sites are closed in the off season. The scenery is always open thogh. Instead of Kenmare, try Westport, another nice little town. Connemara is a nice option from there. Figure that one day will be spent just crossing the country. I know it's only 126 miles from Galway to Dublin, but it ia about a 4 hour drive, and that is on the main roads.

Bill

THANKS FOR YOUR THOUGHTS. I'M TRYING TO WHITTLE IT DOWN. AMONG GALWAY, ADARE, KILKENNY, KILDARE AND DUBLIN, WHICH WOULD YOU RECOMMEND? HOTEL &/OR RESTAURANT SUGGESTION WOULD ALSO BE WELCOME? IS THERE ANYTHING IN AND AROUND SLIGO(3 DAY STAY INCLUDES WEDDING EVENTS AND NEW YEARS) THAT I SHOULD NOT MISS?

THANKS AGAIN FOR YOUR HELP!

It really depends on what you want to see. If you'd prefer city stuff, then go right to Dublin and spend your days there. If you'd rather see the dramatic natural beauty of the west, you might think about basing yourself in Galway and doing day trips into Connemara, the Burren, and west Clare.
I wouldn't spend any of your limited time in Adare. It's 'theme park cute' and full of gift shops and antique stores. And, driving as far south as Kilkenny wouldn't make sense to me.