To ask for best things to see within 1.5 hours of London?

[VeraViolet]

My dd (aged 15) has a French friend coming to stay for a week in August. They met at a German language camp in Germany last year, and the girl then invited her to stay with her family in France. Dd had an amazing time - they showed her all around Paris, and went to a beautiful chateau a short distance outside of Paris.

Now this French girl is coming to stay with us. We live in north London. Our issue is that she's visited London several times before, with her family and school, so has seen all the big sights. We therefore want to find trips outside London we can take her on - most of them will need to be accessible by train/bus, because I work during the week so there'll be no one to drive them.

We were thinking dd could take her to Cambridge (to look round the city and go punting), to Brighton (the Pavilion, the lanes & the new tower) and maybe to Canterbury? Dd loves Salisbury (we used to live there) but we've ruled that out in the light of recent events.

But we need to think of at least 2 other interesting day trips they could go on. Does anyone have any suggestions of the best sights in SE England, or London hidden gems that she might not have seen already?

Not Camber Sands by train, takes about 6 hours from n. London with a bloody long walk from station.
Tenterden by train then steam train to Bosnian Castle...a very British thing to do and Tenterden has lovely shops and restaurants.

Train to Hampton Court goes from Waterloo every half hour. A walk through Hampton Court gardens takes you to Bushy Park.

Some lovely places to eat near Hampton Court. Can definitely recommend The Mute Swan.

Definitely Oxford! Christchurch meadow and the great hall (Harry Potter ) Alice’s shop, Ashmoleon museum, natural history museum, history of science museum and Pitt rivers museum... Bodleian library, punting, retail therapy in the new west gate, Oxford castle etc etc