Umbrian, I don't know about lesser known gardens, but my personal favourites are;
Trebah Gardens
Lost Gardens of Heligan
The Eden Project
Bosvigo
If you like wandering around Garden Centres, then, Bodmin Plant and Herb Nursery is not far away from Trelawney Garden Leisure and one tiny one full of treasures, is Constantine Garden Nursery which is not too far away from Trevenna Cross Nursery.
However, my very best one, which is worth all the trouble of reaching it, is, Tresco Abbey Gardens.
This to me is a magical place.
You can fly from Newquay Airport, or take a helicopter from Penzance, or a ferry from Penzance
I went there a couple of times, when I lived in Cornwall, once in February and once in July.
Both times have given me the most wonderful memories.
Have a look at this website.
http://www.gardensofcornwall.com/Of the gardens they list, that I visited, the only ones that I found slightly disappointing were;
Pinsla Garden and Nursery. A bit run down and straggly.
The Japanese Garden and Bonsai Nursery. Old, dark and boring.
Burncoose Gardens and Nursery. Wonderful R.H.S. show displays, but the gardens and nursery, to me, did not come up to expectations.
Bear in mind that all of these are personal opinions and that the gardens may have been refurbished, since my visits.
Daisy