Since we landed at Gatwick, the first place we went was Nyman's Garden, which is one of the National Trust properties (http://www.nationaltrust.org.uk/). As Americans visiting the UK, one of the best things we did was joining The Royal Oak Society a couple of months ago. If you're planning a trip to England, Scotland or Wales and will visit more than three Trust properties, the membership pays for itself. I really liked this property!
There are extensive areas for strolling, and the photo below shows the first view one gets of the garden. As with all of the photos, click on them to go to full size.
There's lots of information on the Trust site about Nyman's, but in short it's a very romantic property, built into the ruins of a Gothic mansion. The Countess of Rosse lived there until she died in the early 90's, though it's been open as a Trust property since the 1950's.
Leaving Nyman's, the "Garmin Chick" directed us over the river and through the woods to Parham House. I had chosen to visit this garden first because I had followed a series of articles written by the head gardener over a year in Fine Gardening magazine, and second, because the garden is largely geared toward cut flowers for the house, which is something I deal with at work on a daily basis.
The garden was really fabulous, and had lots of quirky surprises, like this life-sized sculpture under the apple tree.
Parham was really a fabulous house and garden, as well, and one I would recommend to other visitors. It is privately owned and inhaabited, but open five days a week. http://www.parham.co.uk/. At this time of year, the lavender borders are just incredible!
In hindsight, we should have allowed more time in Brighton, since there is much more to do there than one would initially expect from some of the travel websites.