Here are some suggestions for a clockwise garden tour starting at Gatwick:

Hever Castle,Edenbridge, Kent
Penshurst Place, Tonbridge, Kent
Leeds Castle, Maidstone, Kent
Sissinghurst Castle, Cranbrook, Kent
Great Dixter, Northiam, nr. Rye, East Sussex
Pashley Manor, Ticehurst, East Sussex
Sheffield Park Garden, Uckfield, East Sussex
Nymans, Haywards Heath, West Sussex
Leonardslee Gardens, Horsham, West Sussex
Polesden Lacey, Dorking, Surrey

Needless to say, doing ALL of them might be a bit much, but at least you now have a few ideas.

If you would like further information or suggestions on gardens or attractions, please feel free to contact me. My email is in my profile (I think!).