Try Enterprise Rent a Car. I have a reservation with this company for a one -way rental from the Galveston cruise terminal to Houston's Hobby airport. The rate is reasonable. I am not shilling for Enterprise but this seems to be the only company that has a one-way program in Galveston.
I also read some nice reports on Galveston Limo, which has reasonable rates to and from Houston's airports to the Galveston cruise terminal.