I lived in Galveston from 2006-2010 and owned a few businesses on the Strand and beach.
My suggestions: Family-friendly dining--Casey's (39th and Seawall). Casey's is the casual-dining option from the Gaido family, who have been Galveston dining institutions for more than 100 years. Gaido's, next door, is their flagship restaurant. Although they don't have the same menu, Casey's still has the same high-quality Gulf-fresh seafood as Gaido's (Landry's and the other chains use frozen seafood from all over the place) and has burgers and other options for the kids. The prices are reasonable (far better than Rainforest) and it's got a great view of the water.
It is not, however, within walking distance of the cruise ship.
If you want to eat within walking distance of the terminal, I recommend the following:
Lunchbox Cafe, 23rd Street about a block off Strand. Locally-owned, artisan sandwiches. If you like gourmet sandwiches made with local, organic ingredients, this is a GREAT place.
Yaga's Cafe, 23rd and Strand. Pizza, burgers, some seafood. Locally-owned.
Olympia 21. At 21st and Harborside. Greek food, also locally-owned. Pricier than the other options, but great seafood and a harbor view.
You can see all of these are locally-owned. There are so many great local options in Galveston, I don't think I've ever recommended a chain restaurant.
The previous poster is correct...in the general "downtown" area, there is a lot of historic architecture. Galveston has the largest collection of Victorian homes west of the Mississippi. Many of them survived the Great Storm of 1900, the largest natural disaster in American history. 1900 Storm Survivors often have a plaque on them that looks like a diamond with a rectangle through it. All of them survived Hurricane Ike. Our former store downtown had 9 1/2 feet of water in it from Ike and our store on the beach sat almost 17 feet off the ground and STILL had almost 2 ft of water in it. Ike was a Category 2 (almost 3) with a Category 4 storm surge. If you're interested in the 1900 Storm, at 21st and Harborside at the Great Storm Theatre, there's a great movie on it and also the island's history with the Pirate Jean Lafitte (the foundation of his home is behind a *ahem* lovely chain link fence on Harborside around 15th Street, I think.)
The Pleasure Pier opened after we moved, but I hear it's fun. Moody Gardens has great family activities. A day pass is $49 and includes admission to the Rainforest pyramid, aquarium, IMAX, and paddlewheel boat.