The Texas City Museum is awesome. The kids I took with me are a little silly... but the museum is awesome.
Just look at the picture. There is a cool kids room around the corner, but they are determined to stick their heads in the cannon.
Stop to read about the artifacts and you will learn even more. And, of course, swing by the interactive kids room!
On Saturdays, you can see the The Galveston County Model Railroad Club Exhibit that is very very well done. (In 11 years of motherhood I've seen a lot of model train displays... and this might be the best.)