The one "must do" at Moody Gardens is the aquarium. The rainforest and 3-D Imax are also nice, but don't miss the aquarium. Schlitterbaun is nearby but they might only be open on weekends until summer.
If I had tomorrow afternoon off of work, I would probably have lunch and a beer at the Spot and then I'd grab a longboard and catch a few waves. But that's just me....
The Spot is on Seawall (around 32nd street). Although if it were me and I had the day off and was going to be in Alvin, I might eat at Joe's BBQ instead.