The "Titanic Belfast Experience" I think is the best exhibit and world's largest dedicated to the Titanic. Highly recommend for anyone going to Belfast. The museum offers a greater focus on the construction of the ship and conditions in Belfast when the ship was built. There's even a ride inside the museum simulating the work conditions at the shipyard. The museum itself is built on the site where the Titanic was built a developing area in Belfast known at the "Titanic District". There is a lot to see and do in this area. There's even the SS Nomadic which is the only surviving White Star Line vessel which was used as a tender to the Titanic in France prior to the transatlantic crossing.
Video from my visit.