There is so much to do/see/eat/buy right in the area, especially this time of year, I don't even know where to begin...
The cruise terminal is just a couple of walking blocks from "old downtown", also known as The Strand. So many adorable and unique shops, places to eat, even attractions such as Pirates! and the Haunted Mayfield Manor. There is always something going on at Saengerfest Park, right at Strand and 23rd, whether it be a crafts fair, or a crawfish festival, or a family outdoor movie night, or (right now) the Lasers, Lights, and Magic in the Park show.
Be sure and venture off the Strand itself -- there are more wonderful shops and delights on Mechanic, Market, and Post Office.
Find out all the goings-on here:
http://www.galveston.com and look here for a pdf map:
http://www.galveston.com/maps/map.pdf
You can definitely watch the ships leave -- DS and I pop over the bridge and do that all the time. We park right by the OceanStar Drilling museum (#16 on the map) and stand there on the pier to the left of the museum (if you're facing the water.)
Hope this helps! I never get enough of that wonderful island.