Ron,
Although the museum is great (especially if you're a TITANIC novice and want to learn a lot), the real piece of TITANIC history is about a 10 minute walk down the street...the TITANIC Pump Room and Dry Dock. Originally build to hold the OLYMPIC Class liners, the Thompson Graving Dock (it's real name) was the largest dry dock in the world when it was finished in 1911. After TITANIC was launched, she was sent to a fitting out berth, and then towed to the dry dock for final preparations. There's a small admission fee, and you can actually walk down steps and walk along the bottom of the massive dry dock. It really gives you an idea of just how big the ship was. The original keel blocks on which the ship rested are still there.
Like I said, the museum is great...and well worth a visit. But the dry dock is a more tangent connection to the ship. It takes about an hour.
Hope this helps.
-Russ