You can’t move for National Trust houses & gardens down here.
A few worth specific mention are: Sissinghurst Castle- home to Harold Nicolson & Vita Sackville-West and a favourite amongst garden lovers. (30 minute drive)
Then there’s Great Dixter, by Christopher Lloyd who was one of Britain’s most talented plantsmen & writers. that’s just 10 minutes away.
Small Hythe Place, 16th century house and home to many – most famously the Victorian actress Ellen Terry is 10 minutes away.
Bodiam Castle (30 minutes drive)