Hillier Gardens & Arboretum - Set in the rolling Hampshire countryside between Winchester & Romsey and  only 4 miles from Crofton, The Sir Harold Hillier Gardens & Arboretum claims to comprise the greatest collection of hardy trees and shrubs in the world.
Hillier Gardens website

Exbury - vast range of exotic plants and trees created by Lionel de Rothschild in the 1920s. One of the yew trees is reputedly mentioned in the Doomsday Book. Famous for its spectacular colours in Spring and Summer, there is also some beautiful colour in Autumn that wouldn't look out of place in New England.
Exbury website

Houghton Lodge Gardens & Hydroponicum   - Fine trees and spacious lawns surround unique 18thC "Cottage Ornée" beside the River Test.  One acre kitchen garden.  Hydroponic greenhouse tour.
Houghton Lodge website

Furzey Gardens - Set in the heart of the New Forest, this delightful informal garden is renown for its year round beauty. A 16th century restored Forest Cottage and 3 play log cabins for the children.
Furzey Gardens website

Wickham Vineyard - A Hampshire vineyard with a modern, well-equipped winery and tasting room, together with a 7.5 acre nature reserve.
Wickham Vineyard website