I agree with what Shanti says above. While I'm not a native Texan, I have been a resident of the Houston area for over 20 years now. It takes me 1 hour and 15 minutes to drive 21 miles to work each day and just about the same to drive home. For frame of reference, we live in Katy and I drive to the Galleria area (more specifically - I work in Williams Tower). Houston traffic is honestly the worst I've driven in and I can compare that to driving in Philly, LA and Denver traffic which are all bad, but in my opinion, not as bad as Houston traffic.
That said, from IAH (or Hobby) to Galveston it is a straight shot down 45 and as long as you don't mind stalled traffic in all lanes during several spots on your journey, once you get on 45, it's really easy.
If I weren't from here I'd use a car service or shuttle service. We find it more relaxing to do the same in Florida when going to Port Canaveral.
When we go to the port in Galveston we drive down and park our car in Lighthouse Parking. Easy to rent a spot online and there's even an early bird discount if you do so.
Happy cruising!