We are not renting a car so we are hoping to stay someplace central to things to do and see.
We arrive in Dublin Monday the 10th @ 8:30 am and then will catch a train. On Wednesday the 12th we will head back to Dublin for a 4 night stay through my work. We are trying to get a feel of Ireland outside of a main city so any recommendations would be great.
We have looked at the Imperial Hotel but don't know if there is a B&B that would be more fun or any other hotel that would be highly recommended.
You will not get a feel of Ireland outside of a large city because Cork is a large city. It sounds like you will have one full day there.
The Imperial has an excellent location for your purposes. Some others to consider would be the Clarion, Jury's Cork Inn, Lancaster Lodge. I suppose it will depend on your taste and budget.
I hope you find just the right place for your short stay.