I'll start with my own favorite: Green Animals Topiary Garden in Portsmouth, Rhode Island. This beautiful estate was my first introduction to the art of topiary. Overlooking Narragansett Bay, Green Animals is on seven acres and features 80 pieces of topiary, including 21 animals and birds. The garden is the oldest and most northern topiary garden in the United States.
Virtual address: Green Animals Detailed information about the gardens can be found at Wikipedia
Moving south into warmer climates, Bishopville, South Carolina boasts another amazing topiary estate: Pearl Fryar's Topiary Garden. The man who built it used mainly unwanted plants, never fertilizes, and seldom waters. His amazing and artistic creations and fountains are made from things he "just found laying around." Read the whole story at Pearl Fryar's
Monkton, Maryland is the home of Ladew Topiary Gardens, established in the late 1930's. The most popular topiary is a hunt with horses, dogs, and the fox clearing a well-trimmed hedge; it is also the most famous single piece of classical topiary in North America.
Here in Ohio, a unique topiary garden exists in downtown Columbus. The Columbus Topiary Park at Old Deaf School features a green tableau of Georges Seurat's famous painting, "Sunday Afternoon on the Island of La Grande Jatte." This unique garden is the only existing topiary interpretation of a painting. Fifty-four topiary people, eight boats, three dogs, a monkey, and a cat are arranged around a real pond. Virtual address:Topiary Park
Great Britain is, of course, the heart of topiary gardening. A few of the most famous include Levens Hall and Topiary Gardens in Cumbria, England (started in 1694) Levens Hall; Canons Ashby, Northamptonshire (a 16th century garden revived in 1708) Canons Ashby; Hidcote Manor, Gloucestershire (1907) Hidcote Manor; Hever Castle, Kent (early nineteenth century) Hever Castle; Knightshayes, Devon (1870's) Knightshayes; and Drummond Castle, Perthshire, Scotland (1605) Drummond Castle. The full list of topiary gardens in Great Britain is extensive and available here: Great Britain's Topiary Gardens
The ancient and skilled art of topiary was, and is, practiced all over the world: from Tasmania, Australia (Railton Town of Topiary, Railton) to Manipur, India (Samban-Lei Sekpil) and Thailand (Royal Palace at Bang Pa); from Costa Rica (Parque Francisco Alvarado, Zarcero) to England (Great Dixter Gardens, East Sussex, Great Dixter); in Wales (Portmeirion, Snowdonia) and France (Chateau de Villandry) and Italy (Villa Lante, Bagnaia; Castello Balduino, Montalto Pavese).
A real-time visit to even one of these magical places would be good for any gardener's soul.