Hi Mueller, I think that it would be hard to say. I think a lot of the interest in Titanic is not just that it was a great ship in her day, but that Titanic's sinking was a stage where human drama was all too real. People like Margaret Brown were certainly known at the time, but it is what they did during and after the sinking that assured their place in history.
If Titanic had not sunk, I probably wouldn't know much about anyone on board; with the exception of the very wealthy (and therefore already well known) people. It's not my place to suggest, but I dare say that those larger than life people like Captain Smith might have faded from memory had they not had the unfortunate distinction of having died on the Titanic. Someone like Guggenheim or Astor had the wealth and already filled the newspapers before their sinking. Titanic's sinking allowed us to see and know of people who, for lack of a better term, were too 'normal' and blended in to those around them. Except that night.
In light of that and in keeping with the scenario you defined, had Titanic not sunk I think the rooms which I would have wanted to see would include the engineering spaces. The grand parts of a ship are nice, but give me the working areas.