If your trip is to League City/Texas City I'd find a hotel in that area that meets your needs. Houston to LC/TC is some distance and during rush hour will probably kill an hour or more.

I usually hit the Hilton Clear Lake - it's a nice business hotel but not near anything (aside from NASA across the street). There's not much in the way of (or much demand) for 4/5 star properties in the area but most hotels are reasonably modern and well kept to expected brand standards.