Belfast

I (probably) have to go to Belfast for a day with work, so I'm going to take my floating bank holiday and spend some time there beforehand. I've never been before - what should I try to see and do while I'm there? I might go to the Giant's Causeway if I can work out how to get there by public transport. People in my team recommended the troubles taxi tour, but I'm not entirely sure about that... Oh, also somewhere cheap and quiet to stay.