Our chicken coop and run sits inside a fenced in garden in our yard in the city. Due to the size of our backyard (25 X 64), the area we had already fenced in for the garden (25 X 11) was the most logical place to put the coop/run in order to be a good neighbor. It was also an area that is largely protected from the Santa Ana winds we're prone to in this area.
As has been already said, chickens will eat your veggies if allowed to freely roam. However, we've used many of the ideas presented by vermontgal and have had minimal problems. As you can see by my avatar photo, they have a secure coop/run inside the garden area. When in their run, they pose no threat to the veggies. Unless it's the end of the season, I do not allow them to range in my veggie garden. Since there are only 3 of them, it's easy to simply call them outside the veggie garden to range in the backyard and shut the gate behind them. Since there is more space, they're happier out there anyway.
The challenge to this plan is that they don't have access to their nest box. This also hasn't been a problem because they've established good nest box habits and they'll usually complain to be let back in to lay an egg. They'll be 3 years old next month and I've not had a single egg laid outside of their coop. However, I work from home and can listen for them. If your plans are to let them roam while you're not home, this could be a problem.
As for the poop. . . yes, when it is fresh out of the chicken, it's too harsh for plants, particularly veggie plants. However, in the larger garden it is no problem. However, their poop can be a plus for your garden. I do not use any chemicals in my backyard. However, I do have a compost pile that is made of garden/yard trimmings and their coop bedding. I use this in my yard, particularly in the veggie beds. I grow some beautiful veggies! Not only that, but my back lawn looks far better than before I had chickens. It's always green and healthy due to their fertilizing of the yard. In fact, it looks way better than my front lawn! Too bad I can't let them out there for a while.