Hi there
Welcome to the community!
At Gatwick North Terminal, there's the Premier Inn, Hampton by Hilton, Sofitel or Yotel. All are within walking distance of Departures. In the South Terminal, there's the BLOC or the Hilton. There is a free monorail between the terminals so it doesn't really matter where you stay as they are all close.
There are also a multitude of local B&B's who offer free shuttle services to the airport. Try searching Gatwick on a site like Booking.Com for those options.
All the best
Mandy