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Carnival and Princess cruise lines (perhaps others) have regular cruises which depart from Galveston.
Gresham House
A Romanesque-style estate that is a Galveston landmark, once home to cotton financier and Galveston magnate William Lewis Moody, Jr.
Texas Seaport Museum
All sorts of railway things to see. It's in the old Galveston Railway Station, and the lobby is a huge period display. A large model train layout is also located in the museum.