Don't forget in Belfast to visit the Queen's Head. It is on Great Victoria Street and is still a gas-lit pub. Quite fun. I think they Odessey was a bit overated and very hard to walk to from Belfast city centre, but you might want to give it a try. Belfast has some nice botanical gardens and is an easy city centre to walk around.
I assume you will be taking the Enterprise service between Belfast and Dublin. That connects up right with the LUAS (the light rail in Dublin) but only the Nothern line. The Southern line starts at St Stephen's Green. In the brilliance of everything, they are totally incompatible systems, with the guage of the rails even being different, meaning the two lines will never meet up.
Of course you have to visit the GPO in Dublin on O'Connell Street, just to see where the Brits smushed the Easter Uprising. You can spend weeks in Dublin. The Guiness Brewery is touristy. The Jameson Distillary is nice if you are into the alcohol as well. There is lots of shopping and lots of pubs. Trinity College is great (go see the book of Kells) if you are into the history. One of the best tours I ever went on was a Ghost Bus Tour that is run by the Dublin Bus Company. It starts right outside the Transportation Offices on O'Connell street. Dublin's got a lot of decent places to eat at all budgets. If you give a bit more about your interests, I can tell you more about what to check out.
I lived in Dublin 2 (about two blocks from O'Connell Bridge) for about 2 years. The number of pubs that I stumbled out of at 2AM... sheesh...
There are two train stations in town, there is the Central Station which is right next to the Bus Depot and then there is Euston Station (I think the LUAS will get you to and from there now, though I can't remember). Euston is where trains to the south country depart from. Also, outside the LUAS to get around surrounding Dublin is the DART. The DART will get you to some very nice sea-side towns like Howth and Bray where a lot of the Dubliners go for a little rest and relaxation.
I didn't get so much to the south of Ireland. I went over to Galway a couple of times. Very nice over there. Got down to Waterford and a couple of other places.