Think most of the other posts cover it. Our eldest is now 6 and we have a 2-yr old too, so have explored A LOT of options!

The National Trust and English Heritage websites (and apps) are pretty good for acquiring targets and finding out about special events.

Some favourites are:
- Knowle Park in Sevenoaks
- Ightham Mote nearby
- Chartwell near Westerham
- The Bluebell and Kent & East Sussex Railways
- Bedgebury
- Camber Sands, Winchelsea, Rye and Hastings
- Sheffield Park - handily close to the Bluebell Railway
- Box Hill
- RHS gardens at Wisley - and the various theme parks nearby - Thorpe Park etc.

Basically any bit of the North Downs, Kent and Sussex accessible via Bromley, Biggin Hill and Westerham (which I think is the most civilised way out into the country from Forest Hill) or for an early morning jaunt the A23, M23, M20 and even the M3 and 4. Lots to do...!