Absolutely hire a car for 4 days as, as much as I love Galveston, 4 days gives you opportunity to see much more of the area. Moody Gardens is a must, even if you don't stay there. NASA is right up the road as are several attractions in Houston proper.
If your family has any interest in history, the San Jacinto Museum and Battlefield is a great visit.
By the way, my weather prediction for August is Hot and Humid. Possibly VERY hot!
Please note that Houston is sprawling area that spreads out into infinity in most directions. Also note that the reason that Houston and the Gulf Coast is ground zero for refining and chemical production so, although very nice in some areas, is quite heavy industrial in others.
Have fun!