Things to see
 

The wife and I are going to Ireland in March. We land in Dublin on March 17th and fly out on the 24th. We are going to spend half the time in Belfast the other half in Dublin. We would appreciate some suggestions on things to do or see. Here is our current list

Belfest:
Giants Causway
Ballintoy Harbour
Carrick-a-rede

Dublin:
Guiness

Please let us know what you think we should see and where we should stay! :)

>> . . . and where we should stay!<<

What is your budget?

>>Dublin:
Guiness<<

If my only interest in Dublin was Guinness -- I certainly would not stay more than one day.

Carrick-a-rede requires timed tickets and they are ONLY issued/available on site the same day (and would not be a place I'd attempt if the weather is windy or wet).

We spent three days in Dublin in February and most enjoyed our time. Without knowing your interests (beyond Guinness), recommendations might not be useful.

Do you want to see the standard first-time visitor sights? There are numerous guide books and websites from which a "Top Ten" list can be collated.

Do you have particular interests? Please share them and you'll likely receive suggestions to make your holiday more to your liking.

With a few more details on your itinerary, it would be possible to give more specific recommendations.

As you list Belfast ahead of Dublin, are you driving north on arrival on the 17th? If not, you will be in Dublin on St Patrick's Day - when the locals (some of them at least) are not known for being at their best behaviour later in the evening.

In Belfast itself, the Titanic Exhibition has become the major tourist attraction in the city. If you are in the city on Sunday, you could check out St George's Market; you could pursue your interest in Guinness at the famous Crown Liquor Saloon afterwards.

You could survive in Dublin without a car for the final few days of your trip unless you wanted to explore the hinterland; a drive to Glendalough through the Wicklow Mountains is a popular outing. Walks to Howth Head and Bray Head are accessible by the DART local rail service from central Dublin.
Trinity College, Kilmainham Gaol and the Georgian squares are all popular to explore in the centre of town; the hop-on hop-off buses are a good way to get around to these popular sites.