From IAH take the toll road straight to 45 and proceed to Webster. I believe it is toll free between the airport and 45. The only toll road that would save you any time is the Hardy Toll Road, but that would only save you a few minutes. It’s a very long drive, and count on it taking at least 45 minutes to an hour.
Rereading I see, I gave you directions from the airport to Webster and forgot about from Post Oak. I would say that was not a good choice for going to Webster. I would try looking for a hotel in League City or Friendswood, or maybe even Kemah or Seabrook.