We are making a return visit to Cornwall next year, but will have a rental car.
Our plans are three nights in St. Ives, two or three nights in Fowey.
(You might want to consider Truro if you don't have a car, since it is supposed to have good connections.).
Cornwall has several estates with extensive gardens - check the National Trust website for a list of these.
They usually tell you how to get there by public transport.
Our short list includes Buckland Abbey, Cotehele, and Godolphin.
Castles to visit include Tintagel and Restormel.
Out on the Penrith Peninsula (extreme western tip) are many neolithic sites.
Men-en-tol, Lanyon Quoit, and the Merry Maidens Stone Circle are the most famous.
Sennen Cove is supposed to be beautiful, Lands End is also beautiful but has been tarted up with tacky commercialism.
Zennor is a charming village near St. Ives, the Tinners' Arms is an ancient pub in that little village.
Mousehole, near Penzance is a lovely fishing port.
I have been researching our trip for many months.
Two useful guide books are Rough Guide to Devon and Cornwall and The Hidden Places of Cornwall.
Transportation is of course your choice but it's a lot easier to see Cornwall with a rental car than to limit yourself to public transportation.