Hi there,
I'm Irish but haven't really done much touring around my own country . So I can' really advice on places to go or on the whole should I take the car on the ferry question.
Petrol prices and road traffic reports can be found here.
Traffic Report Ireland It's a useful site to check up on as well traffic congestion is one of our specialities. I would say avoid the M50 if at all possible especially around the Red Cow Roundabout. (just a tip if you're planning a route.)- it's one of the craziest places in the country especially during peak hour traffic. We don't call it the M50 car park for nothing...it supposed to be a motorway.

So if possible, avoid.
AAireland also offers a route planner which is quite useful to help you get around.
http://www.discoverireland.com/ca-en/ Tourism site. .
Discover Ireland is the tourism site...a lot of hotels offer special prices during the week or maybe even at weekends. But I really can't comment on how much. We tend to get off the island to get a bit of sunshine.

On that point, do bring an umbrella and raingear. If you're driving a car over on the ferry, then you may as well. You'll only end up buying them there otherwise.
This is one site for car rentals...if you do a search you'll find others.
EuropcarHave a look at the prices and maybe you'll be able to make a decision about the ferry.
Personally Dublin city can be seen in a couple of days and it's a busy busy place...lots of people, lots of traffic! If you're looking for a relaxing holiday then I think the west of Ireland would be best. Lots of pretty scenery, you'll find the Irish scene more frequently there than in Dublin and it may even be a bit cheaper. Check the weather though...the west gets the worst of it!! I'm afraid the other tourists or perhaps some of the other Irish who come from the pretty areas of Ireland will be better at advising you than me.
If you do hang around Dublin, make sure you visit Glendalough, Co Wicklow.
Glendalough. Don't miss that! Howth is a pretty town for a walk/hike over looking the sea. But so is Killiney on the other side of Dublin. Newgrange isn't far from Dublin either with a car, as the other poster mentioned. Well worth a visit. I've never found the crowds there to be a problem.
NewgrangeGood luck with it. I hope someone else can help out with places to see.