In many areas you can find a "U-Pick" farms. They usually carry fruits and veggies that grow easily in a given area. U-Pick farms are usually open from Spring until early Fall.
My daughter and I picked fresh blueberries that were extremely fresh and sweet in early August. She loved this outing because it gave her a chance to enjoy the outdoors and eat some fresh fruit. Kids love this!
A helpful website to help you get started: http://www.pickyourown.org/