This is more like a warning than a tourist trap but do be aware that Galveston is much more expensive than other tourist destinations in Texas. We haven't come across free activities during our 2 days in Galveston the way we have in San Antonio and Austin, for example. We even had to pay extra money to have access to the Strand because of the Mardi Gras festivities....
Unique Suggestions: Galveston is a great place to visit so it's still worth the trip but knowing in advance that you'll have to spend more money there than in other cities will probably help make your trip more enjoyable.
Please be certain the handicrafts you are looking at are hand made, by the people of Galveston, and not imports.
I have found there are some shops that buy cheap, sell high and they are not 'native.'