A good starting point would be to look at the visitkent.co.uk website as this gives many options for day trips. East Sussex is nearby too.
I live about 15 miles from Biddenden. It's a nice village with a few tea shops, pubs and restaurants. There are plenty of National Trust places nearby worth exploring. Other than villages and gardens, you don't say what your interests are, so it's difficult to advise. Villages/small towns worth a look include Tenterden, Headcorn, Cranbrook, Smarden, Burwash, Robertsbridge, Hythe and Wye.
Larger worthwhile places include Canterbury, Whitstable, Tunbridge Wells, Faversham (the country's oldest brewery run tours, it's an interesting town and the walks over to Oare Marshes are good), Hastings (traditional fishing port), Dungeness (unique coastal habitat), Hythe (walk along the canal built to repel Napoleon, but never required), Sandwich/Deal/Dover/Walmer for seaside and castles.
Gardens - plenty NT plus Great Dixter, Groombridge, Penshurst Place and Pashley Manor. Check out the National Gardens Scheme nearer the time for local gardens that are open for charity at ngs.org.uk.
The Kent Battle of Britain Museum near Folkestone is interesting.
Castles - Leeds, Hever, Bodiam and Chiddingstone.
Personally, the area that I find the least interesting is around Margate.