A friend got hit by a person making a sudden K-Turn out of a parking space and fractured his hip. This was in Queens. Another took a turn too hot and wound up in a ditch. He did not ride much except in the city and was not used to banked interstate exits. Another, in Dallas, got hit by an SUV that ran a light and wound up in the hospital for a year and needed cranial surgery as well as 30 other surgical procedures. All of them were wearing full gear and survived.
I live in Jersey City, a very urban environment as well. I have been riding for four years. After my first year, I got hit by a car that crowded through my lane to make a light I was stopping for. His mirror took off my handlebar and I wound up hitting a speed limit sign and got flipped into the street.
But, I was wearing full gear, so even though the bike was totaled, I just had bruises. I was riding my new bike a couple of months later, and have done thousands of miles of touring.
All of us also started off on smaller bikes so we could learn to ride properly.
Yes, it is a risk, but to me, it's worth it. Wear full gear, take it slow, on a small bike at first. Ride in the very early morning to get used to riding before trying it in real traffic, and get out of town as often as you can to do real riding. City streets only teach you a few things.