I don't know anything about Dorset, but I can definitely make some Cornish recommendations.
I'd actually recommend staying away from Penzance and Newquay! They've both seen better days! (Unless you want to try Jamie Oliver's restaurant in Newquay.)
The Eden Project is fabulous - I see you've already put it on your list. If you like gardens, there are tons of lovely ones in Cornwall;.
Trebah is my favourite. It's smallish, but lovely. There are lots of other gardens listed
here.
The
National Seal Sanctuary in Gweek is another of my favourite spots.
St. Ives is a lovely town.
Tate St. Ives is there, if modern art is your thing. Even if it's not, the building is well worth seeing. It's gorgeous! Have a glass of wine in the cafe overlooking the beach. The views are stunning.
While you're in St. Ives, have lunch at the
Porthminster Beach Cafe, right on the beach.
Take a drive to
Fowey - probably my favourite spot in Cornwall. If you're into camping, there's a fab site just across the river (on the ferry) in Bodinnick.
Let me know if you have any questions!
(Edited because I forgot to mention the
Minack Theatre!)