Coming out of Dublin theres a €10 charge to go through the tunnel and about €3 to go over the new bridge which you have to pay in 24 hrs. The west coast is nice from Donegal Bay South. Beware of Learner Drivers and take your waterproofs. The place needs a roof on it but the hospitality is great.
You don't say if you're heading north or to the south...so I'll speak for the south :) Don't stay long in Dublin if you're heading into rebel republic country. It's purely for the tourists and expensive. The west coast is stunning, hard, rocky coastlines and Atlantic winds. cheshireguy is right - the further southwest you go, the more addictive it gets. Galway; Limerick; Tralee...and beyond The east coast is softer, sandy beaches with sheltered treelines. The main link roads in the south are often dualled and built recently. The 'N' roads are variable and 'R' roads more like rural lanes. Uneven, poor quality and narrow. Set your suspension for bumpy. I covered over 6k miles of the republic while working / touring in a summer. Beautiful country, beautiful people. Best tasting steaks I've ever had. You make a new friend every day. Quality all weather gear is not negotiable. It rains whenever it likes. Fog is an issue, too. Make time for Cork. Better than Dublin, in my opinion. It floods regularly, being only about 35ft above sea level. Remember it's km/h and euros over the border. The Garda Síochána are cool - but firm with their speed limits. The sun sets later...west coast sunsets are unique.
Im from Dublin and the only thing i would say would be cautious is with your speed, stay within the limits and the speed is in kilometers per hour, there are speed vans on all the major roads.Plus the Garda Traffic cops have a heavy presence on all all major roads...
Thank you for all your replies. I will check out the threads Catkins :-). I am planning on heading south from Dublin then up the west coast then hopefully catching some road racing further north.