In Corpus, I really like City Diner. Casual, very kid friendly, and the food was really good every time I have been there.
I also really enjoyed Laguna Reef (4242 Laguna Shores Rd) when I went. It is about 3-5 miles down Laguna Shores Rd (just on the Corpus Christ side of the causeway between Padre Island and Corpus Christi). Because it is off the beaten path, I think it is a lot less touristy and the food was very good.
Not sure it is white sand but they are referring to Rockport Beach Park. It is in Aransas Bay and behind a jetty so it is not brown water from churning sand like the rest of the beaches in Texas. I'd say it is no more than a mile long. Also, the water is no more than waist deep until you walk out 150-200 yards. The Link
I'd say the Palm beach they built at Moody Gardens in Galveston has white sand.
Snoopy's and dragonfly by the causeway, scoopy's next to scoopy's is the ice cream end of the fried seafood at snnopy's. Dragonfly higher end but huge portions for entrees under $20.
Virginia's on the bay fish sandwich. Only order the fish sadwich, everything else pales by comparison.