Pinus engelmannii (Apache pine) - has just about the longest needles of any pine, and very rare in cultivation in Britain. They have got one that is doing well at Wakehurst Place, so I'm sure you could grow it. Or try Pinus wallichiana or Pinus montezumae if you can't find an engelmannii
Pinus koraiensis (Korean pine) very common in east Asia, the main source of pine nuts, but hardly ever seen in Britain, attractive interesting garded varieties exist
Sciadopitys verticillata (Japanese Umbrella Pine) Quite unique appearance, being the only thing in its family, perfectly hardy, attractive interesting garden varieties also exist.
Araucaria angustifolia (Parana Pine) Related to the common-as-muck monkey puzzle and very rare in cultivation in Britain, some say it is hardy enough here once established.
Lomatia ferruginea - beautiful, rare in cultivation here and doing well at Wakehurst
Embothrium coccineum - ditto
Gevuina avellana - cutting it a bit finer in terms of hardiness, but again very beautiful flowers, usually in autumn
Nothofagus dombeyi, a magnificent large tree, (but will take 600 years to reach full size) unusual in being a broadleaf evergreen with small leaves. Absolutely hardy.
Nothofagus antarctica, a broadleaf deciduous tree with very small leaves giving an unusually open crown, like a birch but more so, beautiful shaped tree. Absolutely hardy.
Eucalyptus perriniana, commonly grown in the cut flower industry but little seen as an ornamental, which is a shame because it is quite bizarre, unique in appearance, and perfectly hardy
Banksia integrifolia, grows tree-sized, really weird flowers, perfectly hardy
Prumnopitys andina (plum-fruited yew) an unusual monospecific yew-like conifer which is more closely related to the podocarps, becoming rare in nature, with an edible berry (dioecious), perfectly hardy
Maytenus boaria, an unusual evergreen from South America, perfectly hardy, rare in cultivation here.
Drimys winteri (Winter's bark), which gives its name to the Winteraceae, a southern hemisphere family of primitive trees and shrubs. An evergreen with an aromatic flower. Perfectly hardy (though would prefer to be in W Scotland) but not too common in cultivation.

You will observe I have a particular taste for southern hemisphere trees.