Titanic Museum is really good and interesting. I thought it would be really touristy but is really well done. We also enjoyed/learned the walking tour of the history of the troubles. Also City Hall is an interesting building with a small museum inside, but wonderful stained glass windows and marble. If you are there on a weekend, St George' Market for food, music and all kinds of goods. It's a pretty compact city to walk around especially the old town area.