Cornwall has many gardens to visit, these are my favourites :-
Trengwainton – National Trust, near Penzance
I especially like the walled kitchen garden, they mix flowers and vegetables in the separate "rooms" that make up the garden. It never fails to inspire me, after a sunday visit to get back into the garden. nb The cafe does amazing food, all home made.
Lost Gardens of Heligan – near St Austell
A must if you've never been before. An amazing combination of walled gardens, walks, tropical valleys. You'll need at least 1/2 day to do it full justice. Their blog is at http://www.lostgardensofheligan.blogspot.com/
Trelissick Garden – National Trust, near Truro
I enjoy Trelissick best in the spring, like many of the NT gardens they have an amazing display of azaleas, rhododendrons, and bulbs. Make sure you explore the nearby woods, if you head down the hill towards King Harry Ferry, and turn left into the wood, you can explore the local creeks.