If you make it to Portrush, do a lap of the NW200. Alternatively head down Bangor direction take in the folk and transport museum, go out round the ards peninsula, ferry across strangford then down to Newcastle take in the mournes etc.
My wife and I went to Northern Ireland about five years ago.
In Belfast I would recommend a taxi tour of the troubles areas and also a visit to the Crown Liquor Saloon .http://www.nicholsonspubs.co.uk/thecrownliquorsaloonbelfast/