This was our embarkation port and we spent a few days here before boarding the ship --- all of what we did was on on our own....but we highly recommend going into he town and spending some time there. (1) there are free guided tours around the medieval walls and towers leaving from the old bar gate (just south of the big shopping mall on the main street) and it was absolutely fascinating - our guide Jake was great and there were only about 8 out of us so we got to ask a lot of questions. (2) took the Jet Boat over to the Isle of Wight --- easy to get around using public transit on the Isle (3) lots of good local pubs/restaurants
I personally couldn't believe how much has changed here --- in the next few years I think Belfast will come into it's own as a tour destination. Do a guided tour and talk to the the locals but for goodness sake don't ask your tour guide if he's protestant or catholic like someone in my group did!!!