when we originally stated looking I contacted TownePlace Suites by Marriott Houston Galleria because joes house says all suites and shuttle to clinic. I called to ask about airport shuttle and the clerk was super nice, very polite, checked on it for me and said yes, they have this.
When I checked my booking later it showed just a queen room so I called and was transferred to the manager. It turns out it isn't an all suite hotel but he was going to upgrade us for no cost. I asked about how to contact them for airport shuttle and they don't have that, they also don't have shuttles to clinic so please double and triple check the information you find on that site. I just keep thinking about how expensive it would have been if we had found all this out after arrival