Hi,
Yes dublin city is a real pain to drive around as it is very poorly sign posted. Just try following the signs for the Airport! Outside of Dublin things get much easier, infact it is hard to get lost! I would recommend Dublin for St Pats but be warned it will be super busy and you will spend more time trying to get a drink than drinking! But, you'll have a good time!
Belfast is worth a quick look and I mean quick. From Belfast you can do a couple of scenic drives i.e Newcastle or the Causeway coast drive. It will take you approx 2 hours Dublin to belfast and another 1.5 hours if you did the senic thing. If you just want to drink dont hire a car and just stay in dublin.
You could be extravagant and price a domestic flight dublin to galway and do a night on the west coast. Prices can vary from £50 upwards to £500.
40

bazboss
Pro tip