Hi Alison,
Indeed not, we have a gorgeous wee country and everyone is very welcoming, you will have a great trip.
There are loads of Hop on Hop off bus tours within Dublin and Belfast, when I was travelling a few years ago I found these really useful in seeing the great places somewhere has to offer and then you can explore a bit more on your own.
Check out Translink at
http://www.translink.co.uk/Translink-Footer/Visitors/ and there is a great visitors pass you can get if your staying 2 or 3 days www.translink.co.uk/Translink-Footer/Visitors/Belfast-Visitor-Pass/
The train runs to Coleraine every hour, and there are some great places to stay in either Portrush or Portstewart rangeing from Hostels to Hotels (see attached welcome leaflet). If your not thinking of staying in the Causeway Coast (which would be a shame) you can get the 08:10 train from Great Victoria Center, Belfast arriving in Coleraine at 09:40, you can then take the North Coast Tour with ourselves for £35
http://glenara-elite-travel.co.uk/got-tour/ and see all the great attractions in one day, you would be able to get a return train to Belfast at 18:19, or you can be dropped off at your accommodation.
If you need to talk things over to get more clarification, please don't hesitate to call on 0044 28 703 54600.
You'll have a great time :)