City Lodge, Africa Sky, Afton House and Intercontinental are where most stay. I can only speak to Africa Sky and Intercontinental as I have stayed at both. Africa Sky is turn-key, Permits, Meet & Greet, Lodging and Food, I understand Afton Is too. City Lodge and Intercontinental (both at the airport) you have have to arrange your permit (do it yourself or use a service like Riflepermits.com), hotel and food. Certainly City Lodge will be more affordable then Intercontinental. There are plenty of places to eat at the Airport from expensive Quills (very good) at Intercontinental to fast food in the terminal. My favorite place for fast food is Nando's, Nothing beats their Pari Pari chicken.

I would recommend that you you stay on the airport grounds. It's easier and safer. I have nothing against Africa Sky, other then the bar is outside and in the winter its cold. But there are just too many off airport robberies around the airport. Until that is completely under control, (and they are making some headway) for me its just not worth the risk.