Galveston....the beach ain't great. But, there are things to do.
I last stayed at the Harbor House...it is on the channel side, next to the Strand. Rooms are nice, and there are several restaurants next door.
You can stroll the Strand...shop...drink a few beers, etc....and shop some more.
Not sure what you and your bride are into.....but for antiques, go thru the Peanut Butter Warehouse, it is full of old junk....furniture, glassware, etc.
There is the sailing ship Elissa, Seaport Museum, etc in the immediate Strand area.
And, I like to stop by Leo's on Broadway....it is a walk up restaurant. He prepares awesome gumbo, crawfish boudan and riblets. It is a local kind of place...you get the food to go.
Get the good stuff to go...then cruise to the Bolivar Ferry landing.....(take the right lane) and park in the lot, by the landing. Then walk on the free ferry, with your Leo goodies. Sit up top and cruise across the channel to Boliver and return. Takes about an hour round trip. If you are gonna feed the seagulls, please do so from the stern of the ferry.
If you are into history, take in Seawolf Park...they have a WWII Destroyer Escort and a Guppy Class Fleet boat for you to see. Or the Railroad Museum on one end of the Strand.....nice exhibits, rail cars, etc.
There are several places on Broadway, with old homes, etc......Bishops Palace, etc.
Or Moody Gardens....tropical rain forest, fish, etc....it is over off of 61st street, by the airport.
I have spent a few days in Galveston...went to school there......drank a lot of beer, and chased a few nurses from the UTMB Medical School. There are parts of town to avoid, due to the crime, etc.
The Stand is a good area....have fun.