Originally Posted by Aviatrix
There is a hotel within the airport complex which is obviously going to be the most convenient... but probably not the cheapest. I think it may be a Marriott.
It is indeed a Marriott - during my years as a non-rev flyer, I stayed there many times. Back then, the rooms in the round section (north tower) were significantly better IMHO than those in the south (rectangular) wing.
http://marriott.com/property/propertypage/IAHAP
Although there area number of nearby alternatives, nothing beats the ability to check out, take the elevator down, then take the inter-terminal tram (or walk) to your departure terminal without having to go outside and/or wait for the shuttle (and especially if your departure is very early in the morning, some airport hotels (budget and otherwise) have limites shuttle service in the early hours).
Trivia: I'll never forget the night that I stayed at the IAH Airport Marriott at the same time as the Pennsylvania delegates to the Republican National Convention - party central)!