You really must make Titanic Belfast the centrepiece of your day, before the drinking starts:
http://titanicbelfast.com/
The European Union refused to fund a penny of it, just in case you were curious.
If you go on a Sunday, you can have Afternoon Tea by the re-created Titanic Grand Staircase:
http://titanicbelfast.com/Explore/wh...Staircase.aspx
It's easily done as a day trip, depending on schedule, if you head out on BA and return on Cu****iLingus