Can someone please tell me exactly how eyesight works in city driving.
Do you mean adaptive cruise control (ACC), or pre collision braking?
The Eyesight manual warns against using ACC in urban areas. It can take Eyesight 2-3 seconds to react to a new object in its field of view. A car travels 64-93 feet in that time at 35 mph. Also be aware that the cameras only see 12 degrees either side of the centre line which means at the bumper they only see from inboard of the lights, not to the corners. A car can come well into your lane before the cameras pick it up.
Pre collision operates in 3 stages, first it emits an audible and visual warning, followed by moderate braking and then it slams the brakes on full force, probably far harder than you have ever done, unless you take a cancelling action - manually brake, swerve, or accelerate. How long each of those stages lasts depends on the closeness of the object and the speed differential between you and it.
You should not be relying on it to brake for you. Eyesight is designed as a backup for when you make a mistake. It is not an automated braking system, or autopilot. Driving is your job.
If you haven't read the Eyesight manual and watched the DVD, I strongly urge you to do so. It has quirks and limitations you need to be fully aware of. You might also try driving at a few stacked up cardboard, or foam boxes at low speed to see how the system reacts and get used to the warning buzzers, flashing instruments and anti lock brake pulsations.