A half day's drive can get you all the way on the other side of the country!
It's only a couple of hours to drive to Galway and about three hours to drive to Cork city. There are a lot more options of nice rural towns and villages in the west country. It's definitely better for that kind of thing.
If you want to stay closer to Dublin, Kilkenny is a nice town. There's a castle, it's the home of Smithwick's, and there are lots of shops and restaurants.
When I came to Ireland with friends a few years ago we stayed outside Galway in a village called, Oughterard. It was really lovely and was literally on the doorstep of Connemara, so lots of countryside to drive through. My parents stayed there when they were here visiting and they stayed here:
http://www.riverwalkhouse.com B&Bs are very affordable in Ireland, so you should have no problems finding a place to stay.
I'm REALLY surprised you've found automatic rental cars for that cheap. I think we spent about 50 euro a day for one. Be wary about renting the car. Have your boyfriend do it, if possible. If you have to do it then take pictures of every inch of that car so when you return it they don't charge you for scratches and take out the extra insurance. US credit card companies don't cover international car rentals in Ireland and the car rental companies know this. Most Americans don't. If they can, they WILL try to scam you.