We live in the nearest town (Horley) to Gatwick and there are a number of guest houses. The Tudor Rose do car parking and transfer, the closest I think.
There are other "posher" hotels nearer the terminal but if you are staying for one night you might not need "posh". Horley is about 5 mins and Crawley 10-15 mins. Travel Lodge is at Lowfield Heath en route to Crawley, 5 mins away. the Gatwick Manor (Travel Inn) about 5-10 mins. dont forget also that if you have a taxi after 11.00 p.m. it is more... cost us £12.00 for a taxi to home and we only live 5 mins away.
If I had the room I could do a b & b! If you need any help for looking dont be afraid to ask.
Sue