I live in upstate NY on southern border of Adirondacks. I would like to share what I know to work here. We are speaking of edible shrubs here, or small trees. Not the cane fruit, edible ground covers, edible vines or cultivated fruit trees on dwarf rootstock.
Honeyberry already has been mentioned, I have not grown it yet.
Goumi: My favorite shrub is the goumi. It never spread like the invasive relative which ripens in fall. Sweet scarlet goumi already ripened its fruit. They are larger and taste like watermelon fruit roll up with hint of cherry to me.
Currant: We did buy the golden currant from the state agricultural department but the best plant to rival invasive honeysuckle is the clove currant. It smells of cloves and carries on the wind. If you want the scent combined with edible fruit I believe Crandall clove currant is the best match. Goumi is said to smell but it is not strong for me.
Chokecherry: it is a shrub and not a tree. Aronia is a black fruit I do not have experience with but our native red chokecherry is very nice. I believe people confuse it with black cherry which tastes medicinal. Chokecherry ripens around a month earlier. They both turn dark when ripe which helps cause confusion. Chokecherry tasted like a real cherry to me with some variability.
Viburnum species. Although not that tasty, highbush crannberry, nannyberry, and others can be grown.
Highbush blueberry: very pretty in spring and fall. You can get fruit from just one plant. A pollinator creates more fruit.
Pawpaw: it can grow up north, seeds die in winter and the plant needs protection from mice or deer and from the sun till older.
Dogwood: I found silky dogwood growing by a swamp and it is said to be edible although the fruit looked metallic blue so I do not feel comfortable eating it.
Bush cherry: carmine jewel, Romeo, Juliet, Jan, Joel, sandcherries. Canada is working on breeding sweet bush cherries and so are northern states. You need to cage these till older to protect from deer.
Elderberry: we got American from the state agricultural department.
These are the fruity shrubs I have experience with here, and success.