The North Carolina Urban Forest Council sponsors educational workshops across the state and the state Urban Forestry conference (members get a discount to events). Check out its events here.
NC Cooperative Extension is a statewide program through NC State University with a presence in every county, providing expertise on a variety of topics as well as workshops and events. You can find a complete list of events here, where you can also search by county.
The NC Native Plant Society is a volunteer organization with chapters in various locations. Besides being a good source of information on native species choices, they are also quite active with various fieldtrips and events listed here.
Alliance for Community Trees is a national organization focused on urban trees and is a great resource for information. It also keeps an up-to-date list of big events across the country here.
The Forestry & Environmental Outreach Program is based at NC State University and presents a variety of programs to a broad audience, from professionals to teachers, landowners and others. The upcoming events are listed here.