I have an 8x10 garden in my yard, but I am expanding it to about 8x15 this summer. Produces more than I can eat, but the neighbors love that.
Zucchini and squash take up a lot of space. I had two zucchini that died about halfway through the summer (I think I have a grub problem), but that each produced about two pretty large ones each week. They also took up about a quarter of my garden. I also did squash and cucumber, and wrapped the vines around a tomato trellis. Produced a lot in minimal space until beetles got to them.
Tomatoes are obviously easy, but you want to make sure you pick any large and ripe ones before a rain storm. If not, they will swell up with water and get splits in them.
Green beans are easy, I prefer to sprout the seeds in wet paper towels in a ziplock then transfer to some seed trays a few weeks before recommended planting (do this with all of my direct sow seeds). This means I get them in the ground about 3-4 weeks old, and get one extra harvest off of them usually. Use stringless bush beans, not pole - pole look ugly later in the summer.
Herbs are also great and easy, just make sure what you plant isn't impossible to kill, like mint. I only keep mint in a pot. Basil is great, grows easily just dropping the seats in dirt, and if you can't figure out how make amazing stuff with it you are dumb - pair with lemon and sugar, steep in olive oils, tomato sauces, asian food, etc.
I live in an urban river basin in Newport, KY, so our ground stays pretty warm since there are a lot of buildings and large trees which prevent heavy winds from drying out the group. Make sure you keep your ground moist but not saturated, and check for grubs, beetles, and that sort of stuff when you are turning soil and picking things (under leaves, at limb joints, etc).