Premier Inns have 2 hotels inside Gatwick Airport near the North Terminal. The great advantage is that you can walk from either hotel into the terminal with just hand luggage in a few minutes without having the expense of a shuttle bus. It doesn't matter if you really want the South Terminal because the free and frequent monorail will quickly take you there.
The cheaper of the 2 is the one on Longbridge Way. Although the other one immediately adjacent to the terminal is much newer and closer, this one is less than 10 minutes walk along an easy path. It's also built in traditional style – all on one floor. There's also quite a tempting breakfast deal – if you have time before your flight!