You have quite a wide choice. The closest training airfield to Gatwick is Redhill, which is actually tucked under the northern edge of their zone. There are several schools there. Have a look on the
Redhill Aerodrome web site for details.
Going clockwise around Gatwick from there you also have Biggin Hill, Rochester, Lashenden/Headcorn (both of which may be a little far perhaps), Shoreham, Goodwood, Blackbushe and Fairoaks.
Redhill, Biggin and Shoreham would be the three most practical ones to get to by car from Gatwick.
Go and have a look at several schools and pick the one you feel most comfortable with.
Oh, and have fun!