If you mean Weald village, then there is no way that is walkable to Sevenoaks station - it is probably 3 miles away and up a killer hill! I think that most people from Weald would get the train from Hildenborough. It is still a drive away from the village, but I guess that parking is much cheaper than at Sevenoaks.
White Hart Wood is probably just about walkable, but it would be a bit of a slog in the winter. It is over 1.5 miles, but a nice flat walk. Don't believe the estate agents about a shortcut. If you put the two points into Google maps, you cen see the route you would have to take - you may shave a couple of minutes off by going on the back roads rather than Tonbridge and London Roads, but it won't be much.
If you can deal with the commuting issues then that is a lovely part of Sevenoaks with access to the common and the nicer, quieter end of Knole Park. You will also get a bit more for your money than in equivalent roads in central Sevenoaks.