Recommendations and Transportation Advice?

I recommend Rick's Ireland guidebook to give you sightseeing details about these destinations. See also videos at http://www.ricksteves.com/watch-read-listen/video/tv-show. A sidetrip to Newgrange, for instance, can be done with a bus tour.

Trains do spoke out from Dublin, so they could work for a few day trips. However, train time from Dublin to Cork is 3 hours and then a bus connection from there to Kinsale takes one more hour. See our Ireland rail page for a round-up of train, ferry, and flight info and links. Flying Dublin-London can be quite cheap. In addition to the Irish rail link on that page, How to Look Up Train Schedules Online gives you the DB train schedule link and tips for using it.

As Laura mentioned, Newgrange, Trim and other sights in the Boyne valley can be included in a bus tour from Dublin. To the south of Dublin, you can also see the Wicklow Mountains, Glendalough and Powerscourt gardens by bus tour.

Thanks! I am new to this site so I'm still getting familiar with things :)

The highlights for us in Dublin were the Kilmainham Gaol tour, the Natural History and Archaeological Museums, Saint Stephens Green.
An easy and worthwhile day trip is to take the train to Belfast, Northern Ireland. It's a great city with lots to see, good food too. The free City Hall tour is spectacular, and a Black Taxi tour is an enlightening way to spend a couple of hours. We got the train at O'Connell Station at 8 in the morning and were back in Dublin by 7 pm, a great day.
There are lots of inexpensive flights from Dublin to London, be careful about carry on luggage size, etc, and imho it is not worth considering the ferries, it may cost you a bit more to fly, but time is money. Look at Aer Lingus, Ryanair, etc.
Have a great trip!