Pumpkins and other squash. There is a pumpkin farm 2 minutes from my house
and in my yard I have grown excellent hauls of spaghetti squash, acorn squash and zucchini.
Kale also grows really well. A very nutrient dense green, it can be used just like spinach. I froze a bunch and I chop it up very fine and add it to soups, stews and quiches. Remember, flowering kale is also edible and it looks really cool. Slip some in to a flower bed and nobody will know it is really an eating veggie
Herbs. Herbs are basically tasty weeds, so if your growing conditions are iffy, start with an herb garden. You will be pleasantly surprised. I grow Greek oregano, chocolate mint, chives, thyme, lemon thyme, sage, and rosemary. Basil is great too but it is an annual and will have to be replanted. Spicy globe basil is really tasty.
Cucumbers. I have tried bush variety, vine type and even lemon cucumbers. All grow very well but beware....SQUIRRELS like lemon cucumbers. NO FREAKING JOKE. I thought my plant was a dud until I caught one of the evil fuzzy tree rats making off with some of the little yellow buds.
Things I can't seem to grow...
Peppers. I either plant them to late and the fruit never develops or I plant them too early and the frost gets them.
Tomatoes. Unless I plant an early variety, I don't get much for the trouble. I think it has to do with our short growing season due to the cold nights.
Melons.Maybe something with my soil? Who knows. The darn things never grow.
Other things growing well in my yard...
Grape vines. I have 2 and one is a freaking monster. Lots of grapes but it is hard to get our share away from the tree rats.
Pear tree. I only have one and thought I needed a pollinator. Apparently one of my neighbors must have one because we have been getting fruit from it for a couple of years now.
Apple trees. We bought 2 about 4 years ago. Last year we started getting apples.
Day Lilly. Apparently you can eat the tubers, but I use them for decoration. They grow really well in crappy soil and are drought tolerant.
Japanese Spirea. An ornamental shrub with purple flowers in fall. Bees LOVE this plant and mine are covered with all different breeds of bees whenever it flowers. It spreads like crazy so you may have to dig up new plants. I just give them away to friends. It is really easy to prune.