I have to agree, in the loudest possible terms, that you should NOT let the cat outside in a city. The life expectancy is just so much better inside, as well as general quality of life. The risk from cars is huge, of course, but the risk of disease is so much more as well. And then there is getting into fights with other cats, feral dogs, raccoons, etc… And then there are sick people (one of my neighbors had a kitten who was shot and killed by a neighbor with a pellet gun, for example)… there are risks like getting into chemicals and poisons, or eating rodents that have eaten chemicals or poisons… Really the list of dangers is endless.
The fact is that most cats do fine indoors. Two of my three cats started out as strays. Indigo never goes near the door. He lived on the streets and has no desire to do that again. He enjoys looking out the window, but will run the other way if he’s near a door that opens (to the outside). The other one, Cory, will try to escape from time to time. When he gets out he just runs to the nearest grass and starts munching. You can buy cat grass to grow indoors if your cat likes that. For the most part, these two cats enjoy chasing each other in the house, playing with their catnip mice, lounging in patches of sun by the windows, and chasing laser pointers. My third cat is 18 years old and has always been an indoor cat, and has never expressed any interest in going outside.
When I was growing up we had several indoor/outdoor cats. When I turned 18 we had 2, and I took them with me and they became indoor-only cats. Both eventually died of feline leukemia, which they had obviously caught during their time outdoors (one of the cats we had when I was a child died of it, too.) but not before they lived many very happy years as indoor cats.
Just get lots of toys for them. The long wands with string and feathers at the end are a great way to exercise a cat, as are laser pointers. I also have several velcro-closure refillable catnip toys that keep them entertained for hours (their favorite being the tiny teddy bear). We also have one of those kitty towers for them to climb on. And they adore their SuperScratcher thing (also by SmartyKat) which is made of corrugated cardboard. They scratch the hell out of that thing, and even sleep on it.
(Edited to add: I agree about getting a second cat. Two cats playing together and keeping each other company keeps them both exercised and entertained so they don’t turn to destructive behavior out of boredom.)
I know I’m going on and on but I really, really think that it’s wrong to let a cat outdoors (except perhaps on a harness and leash, if your cat will tolerate it) in anything but a rural environment, and even then I’d be scared about predators, and worried that the cat would kill too much local wildlife.
As a bonus: indoor cats don’t get fleas!
A few quotes: “The Humane Society of the United States was quoted in 1992 estimating the average life expectancy of free roaming pets to be between 3 and 5 years, while indoor cats can commonly reach ages of 17 years or more.” and "According to the Santa Clara Valley Humane Society, 57% of all the animals found dead on the streets of San Jose in 1996 were cats. "