Oh, good, you can use the link about what to do with a two-year old in Houston. It has very good advice.
Bring your son's bathing suit and sunscreen. Hermann Park has a fabulous water play area, with fountains to run through.
We started taking our daughter to Children's Hospital a week before her second birthday. (She just turned four.) During the past two years, we have not run out of things to do.
Yet one more thing: There are at least four toy stores in Rice Village, including the local Five and Dime (which has the least expensive toys).
Yet one more food thing: The Best Western has fridges, if you decide to stay there. The Children's Museum allows for picnic lunches, so save the money by bringing your own. Save even more money (on parking) by taking the light rail, which stops a few blocks from the Children's Museum.