Fagus

The native beech of eastern North America, from Nova Scotia and southern Ontario south to northern Florida and eastern Texas: a large, slow-growing, long-lived forest tree with smooth, light grey bark, a dense crown, golden-bronze fall colour and small, sweet, three-sided beechnuts that feed a long list of wildlife. Check its health in your area before planting. Wikipedia reports that beech bark disease has become a major killer of beech in the northeastern US, and that beech leaf disease, caused by a nematode, was found in Ohio in 2012 and had spread as far south as Virginia by 2022, severely damaging American beech. Its shallow roots and dense shade also leave little room for anything beneath it.

A large, long-lived deciduous forest tree of temperate and montane Europe, prized for its dense domed crown, smooth grey "elephant-skin" bark, and glossy leaves that emerge silky-edged in spring and turn warm russet in fall. POWO (Kew) records it as native from France, Germany and Great Britain east to Ukraine and south to Italy, Sicily and the Balkans. It is one of the great cathedral-canopy hardwoods of Europe and an unrivalled clipped formal hedge - but it is a true forest tree, not a small-garden specimen, and the honest catch is the shade it casts: very dense, with shallow, greedy roots, so little will grow beneath an open-grown beech.