Hi there, WELCOME!
I feel ya completly with your space constraints!! I have a 42X140 lot...there is 4 feet of yard on one side of the house, and 8feet on the other; then behind that is another little house on the same lot and a two car attached garage with rear drive. I have privacy fences all around, but I'm not keeping any secrets. My neighbors can see everything I do from their upstairs windows, or their back porch.....just the way it is. But you know, you're a city dweller too!
I keep silkies and showgirls in my garage. They don't fly, which is great. Other birds can get right over a privacy fence if they want to. Mine are notoriously bad layers!! GREAT broodies, they'll sit on unfertile eggs for months!!!!! I am hatching some bantam Aracauna right now....you might message "Little Ameraucana Mom" on here and ask her how well they lay, and if they go broody as frequently as silkies. The eggs are a pretty sea green, and they are mediumish.
They don't have an outdoor run... I have a ton of big dogs in the neighborhood and half the time they're loose... I lost my entire flock (even being in the garage) earlier this spring. The three neighbors dogs came right through the window to get to them. Curious darned Huskies....Instead, when I go out to garden, I let the girls out and they do their picking and dust bathing. When I go inside, they go in the garage. I'm usually out gardening for hours....they seem happy.
Maybe you could post some pictures of they layout of your property, and we could help brainstorm ideas with you?