Black-cap raspberries (the feral sort) are very flavorful, and productive even in somewhat shady parts of my
yard. You don't need much space to get a lot of fruit, we have a half-dozen canes around the edges of the yard, and in season it is more than my family can consume fresh from day-to-day, so plenty to freeze or can. They are not bothered by pests or disease. You do need to prune them to keep the "whip" ends from rooting and taking over the yard, though.
Redcurrants likewise are very productive and flavorful, thought they are very tart so better for drinks/jellies/baking than straight eating in my opinion. Very easy to grow for a fruit that is so expensive at the markets. They propagate easily and do sprawl if not pruned, but do not spread aggressively like the black-caps.
Rhubarb is an attractive plant that needs little care to come up year after year, just split it up like you would a hosta every so often.
Concord-type grapes produce a lot of fruit all at once, probably the greats pound-per-square-foot of anything it the yard. However, they are bothered by fruit flies and fungus, which reduces the actual usable harvest substantially. They also really like my neighbors' side of the
fence more than mine, and they are not so keen on the fruit.