I haven't been to Mobile or Galveston, but New Orleans' port has some good points. It's near the French Quarter, there are several hotels nearby should you wish to stay overnight before or after the cruise (very convenient) and, best of all, if the wait in the cruise terminal gets long, you have access from there directly to the Riverwalk Mall.
Another thing to consider besides the ports is which ships depart from each. In my opinion, the newer ships tend to be better - nicer, cleaner, better atmosphere onboard, and perhaps better food.
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