Comprising 172 acres on the University Of Virginia's Blandy Experimental Farm, the Orland E. White Arboretum was designated the state's official arboretum in 1986. Established on the site of a plantation, with a visitors center in a house that originally served as slave quarters, the arboretum is a nature lover's delight throughout the changing seasons, with plant species from all over the world. And to top it off, admission is free.
If you go:
Open every day of the year, dawn to dusk. Office hours are Monday through Friday, 9 to 5. There are also many special programs, both day and evening, ranging from a haiku walk and write to a moonlight walk and stargazing with a telescope. A fee is required for these activities.
Links:

400 Blandy Farm Lane
Boyce, Virginia 22620 USA
blandy@virginia.edu
Phone Numbers:
Blandy Experiemental Farm
+1 (540) 837-1758
+1 (540) 837-1758