Join Date: Jul 2007
Location: San Francisco/Sydney
Programs: UA 1K/MM, Hilton Diamond, Marriott Something, IHG Gold, Hertz PC, Avis PC
Posts: 8,170
Presuming you're not saying near IAH, the other option is to price two one-way, one-week rentals - one from the airport to an Avis near where you are staying, and another from there to IAH. This may work out being (much) more expensive, or it might worth out being cheaper.
The advantage of returning and re-renting from a local Avis is that it's generally easier - you will definitely be able to keep the same car, and you won't need to worry about putting gas in it before 'returning' it (they'll just mark is as full for both the return and the pickup, regardless of the real level).
The disadvantage (other than the potential price difference) is that if you do want to try and change cars you're likely not going to have a good range to pick from...