Biltimore Estate is unbelievable. Definitely a must see. Also Asheville is home to the NC Arboretum with its beautiful walking trails and plants. The Arboretum is just off the parkway.
The North Carolina Arboretum
Just down the road from Asheville is Village of Flat Rock. Home to the Carl Sandburg Estate. The home is maintained much as the Sandburg's left it. Also Mrs. Sandburg raised prize winning goats. A small herd of goats is still maintained on the grounds. Your two year old would probably like that.
Carl Sandburg Home National Historic Site (U.S. National Park Service)
About 15 miles from Flat Rock is Dupont State Forest. There are many beautiful hiking trails and waterfalls there. Triple Falls is probably too difficult with a 2 year old, but Hooker Falls is a nice leisurely walk from the parking lot. Triple Falls and Hooker Falls were both featured in the film, The Last of the Mohicans.
NCFS - DuPont State Forest
Finally traveling from Dupont State Forest towards Brevard is Pisgah National Forest.
National Forests in North Carolina - Pisgah National Forest
There are many beautiful hiking trails and waterfalls there also. Several falls are very easy hikes (Looking Glass, Moores Cove and Sliding Rock)
» Pisgah National Forest waterfalls near Brevard WNC Visit Brevard NC
Your two year old could easily make all of these.
We go to the Asheville/Hendersonville area at least twice a year. We just love it.
Tom & Deborah & Winston Schnauzer