Until half-way through the twentieth century, American garden design was strongly influenced by European traditions - English, Italian and French. Initially, first generation European immigrants built gardens in North America according to the principles they had learnt back home. Later on, American gardeners learnt about garden design from European books. After 1950, America took a lead in modern garden and landscape design. The lead came from the landscape architecture profession, which had a wider involvement with garden design in the United States than in most other countries, where landscape architects have tended to concentrate on public open space projects. American landscape architects were also leaders in city planning. It is the only country in the world where two presidents (Jefferson and Washington) have had a significant involvement in garden design (rather as kings did in Europe).
The North American continent is large with a very varied topography so it is unsurprising that the native flora is also very large and varied.
See Gardens to Visit in the US - and here are some key US gardens: Biltmore Estate, The Arnold Arboretum, Central Park NY, Dumbarton Oaks, Monticello, Mount Vernon Estate and Gardens, Old Westbury Gardens, Longwood Gardens, Getty Centre, Naumkeag
Because of the enormous dominance of private cars in American transport, other methods of garden visiting are comparatively undeveloped. You can travel from city to city by plane or train but after that it is usually necessary to hire a private car. Compared to most European countries, there are few organised coach tours for garden travellers. Within the largest cities there good metro and bus systems.