I live in Suffolk and I've often dropped people off at Gatwick before going on to enjoy the rest of the day. My absolute number one favourite place has to be Brighton, which is just 28 miles from Gatwick Airport. (If you don't fancy driving, you can leave the car at Gatwick Airport and hop on a train).
Brighton's star attraction has to be the Royal Pavilion, which is probably the most opulently furnished building in England!
http://www.royalpavilion.org.uk/
Preston Manor is worth a look as well.
If you don't want to go to the far side of Gatwick Airport, then a slight detour to your return route will take you to Hever Castle:
http://www.hever-castle.co.uk/
or Chartwell:
http://www.nationaltrust.org.uk/main/w-vh/w-vi sits/w-findaplace/w-chartwell/
For somewhere that's distinctly different to anywhere else, but full of history, head off the M25 for Chatham's Historic Dockyard:
http://www.chdt.org.uk/
Chris