I have a big family (siblings nieces and nephews etc) and every year we try and meet up somewhere in the country for a camping get together (easiest way of doing it with 30+ of us). Think done most of the national parks now in England (except the one I live in!) haven't done New forest and South Downs. Is there plenty to see around there? Good walks etc. not into the typical tourist traps tbh- every NP has them and generally wise to avoid IMO!
I have a lot of good memories of that part of the world, growing up in East Sussex, day trips to the coast often involved walks on the downs north of Eastbourne and to the west.
Birling gap is worth a visit before it completely disappears into the sea and the area around Cuckmere haven has some nice walks as I remember.
If you're interested in buildings and walls built from flint it's the place to be.
And a lot of Roman history around Arundle and Chicester, further west you're into
@doobin country.
Sad thing is its a overpopulated part of a overpopulated island and usually quite busy!