Anything I absolutely must do/see on my way through the Houston Airport tomorrow? I’ll be there for about an hour.
Is that an hour from scheduled landing to scheduled takeoff? Actually, now that I think about it, you may be stuck there for a little longer than an hour with a tropical storm scheduled to hit around the Houston area around noonish.
Anyway, if it is from landing to take off, and no delays, then really, not much time to do much except eat (IMHO). You will spend a good 30 minutes of that getting off one plane, walking to your next gate, and boarding.
Absolutely, must get out of Houston as quickly as possible!
Which Houston airport?
IF you had more than 1 hour (more like 3 or 4) and you were flying in of/out of Hobby, then a good place to visit would be The 1940 Air Terminal Museum at William P. Hobby Airport. A lot of displays on airline history of Houston is located there. It’s located a few miles from the HOU terminal so you would have to take a taxi to get to it. Be worth it, though.
I was flying through Bush International, and I ran into absolutely no issues. It was a rather full airport and a rather full flight both ways though.