The strand is one block over from where yall are docking, and there are some nice shops on it.
I agree with staylor--Pappasitos for fajitas and margaritas! Luigis on the strand for italian, and gaidos on the seawall for shrimp. the beach is not close enough to walk, but you could take a cab there or to Moody Gardens--a museum, rain forest, aquarium in giant pyramids. Johnson Space Center is about 30 minutes up the road, and you would go to Space Center Houston there (the public area of JSC)
Welcome to Texas, Y'all!