How tall does this have to be?

No more than eight feet or so. Lower and I can see the house, higher and I can't see the mountaintop.

How about Juneberries?

I don't know. What are they? Will they grow in NC?

Sure! They are also called shadblow, saskatoon, serviceberries or sarvisberries, have you heard of any of those? Amelanchier spp. Similar to blueberries except not needing such acid soil, also very ornamental, and native to our part of the world. Underused.

Here is a link that might be useful: Amelanchier arborea

you won't be happy w/just blueberries they grow SLOW.

I would suggest a mixed screen where you can throw a few fruting plants (e.g blueberries) in. We have a screen of hicksii yew, camellia, hollies, rhodendron, azalea, and bay berry, with blueberries, thornless blackberries, elderberries, highbush cranberry, currants, gooseberrie, aronia, raspberries mixed in. There area also a few fruit trees (apricot and pear). It is also underplanted with some bulbs, iris, hosta, and astible.

Thanks for the info on Juneberries and on the mixed screen. This gives me something to work with.

I second the suggestion of serviceberry/juneberry/amelanchier for a screen. The clump bushes typically grow over 10ft high and provide very nice blueberry-like fruits in June. Many say they are tastier and sweeter than blueberries, though the seed is bigger. There are many types of cultivars. Choose one with the height range, and the looks, that you are interested in. They come in trees and clump bushes. I have never seen the trees, though i have seen the clump bushes used for screens. They do lose their leaves in the winter so you do need to pack them in, for a better winter screen.
Always an...Angel