I organized a post two years ago with then-current information about a number of hotels near the airport. I updated prices last year, but I hope it's still useful for general information, web links and shuttle information. I also specified which hotels I've stayed in and so can speak of from first hand experience.
Tripadvisor remains a good source of reviews. The neighborhood lacks many restaurants or other things to do. But it's the place to stay for early morning departures.
A minor correction to Steve's response above. The Crowne Plaza is not in the airport. It's close by, though, in the same neighborhood as the Cervo and the First between the two terminals.