Headcorn! Great airfield to visit and just watch at, or there are a couple of clubs there to fly from. Someone also mentioned that you can fly the Tiger Moths there (with Brendon O'Brien if this floats your boat!).
There is also a cafe, a bar on site, a museum and it is a nice place. I have never landed there but I pop there on occasional weekend with the camera!
Rochester is also not a million miles from Maidstone, and of course you have Biggin Hill, Lydd and Manston a bit further away.