Any sized backyard can accommodated a flock. Unlike roosters, hens are relatively quiet, only emitting a low cooing or cackle when startled. With a small flock like this, they do NOT smell. I know that Fayetteville and Rogers specifically allow 4 hens to be kept for backyard egg production. However, it's a good idea to call your city and learn the specifics of any pertinent ordinances.
Approximate costs:
My help and labor - FREE
4 hens - $10
Coop materials - $50+ depending on design
Feed costs - $8 per month
Return:
2 dozen healthy, fresh eggs per week
The ability to recycle your food scraps without having to compost
The enjoyment of watching your own chickens scratching about in your backyard