You're unlikely to get anywhere within 10 miles this late in the day; they're all usually booked up months in advance in an airshow year; it's the exhibitors you see, they bring their staff in for the week and want local accomodation. Suggest you try somewhere with good rail connections eg Basingstoke, Dorking, Reading, possibly Bracknell as the roads usually get clogged up, but the walk from Farnborough Main station (Waterloo - Southampton line) and North Camp or Farnborough North (Reading - Gatwick line) isn't too bad.