I second Tom's suggestion of Royal Ashdown. Top class.
Nearby is Crowborough Beacon which is a very decent course with a number of heroic holes (2nd and 6th), at which Conan Doyle (Sherlock Holmes) was once Captain. As well as the course itself, it's a lovely place because you cross a number of lanes and footpaths and you meet people out walking their dogs or riding which adds to the sociability if you are out on your own. The views from the clubhouse on a fine day are magnificent.
You're not all that far from The Addington which is between Croydon and Shirley. It is a terrific course, full of fun and character. It seems that it is going to be developed in some way, so go now while it is still quaint.
Another course you might want to consider near TW is Piltdown, which have not played, but it has been recommended to me by many. It is a rare bunkerless course as is RAF.
Of the modern courses, East Sussex National at Uckfield is not worth the green fee, in my opinion, but Chart Hills at Biddenden is one of the better new courses, in my opinion. It's a Nick Faldo course (with help, of course) and it does have some very individual holes and quite a lot of character. If I remember rightly, however, you have to pay a green fee of something like £200 for a tee, whether you are a 4-ball or a single.
Your nearest links courses are Rye (A1) and Littlestone (a nice course with a sterling finish).
There's an Abercromby course at Knole Park just outside Sevenoaks, which i have not played, but others on GCA have warmly recommended.