Part 1: Exile
Finding an exit from the City was easy. Safety was the primary concern of the Founders. After all, they had lived through the Breakdown. Unlike builders in the Crazy Age, they assumed that their City would fail catastrophically at some point, and people would need to leave in a hurry, so anywhere along the wall, you are no more than 5 minutes from the nearest exit.
Finding an entrance was a different story. Clearly, there must have been one when the City was founded, although perhaps it was just where the wall wasn't finished yet. It was not clear whether it was part of the Founders' original design that you shouldn't be able to come back in the exits. Personally I suspect that was changed later. Still, that was long enough ago that no one remembers anyone entering the City ever.
Part of the reason is that all the exits are monitored all the time. That isn't to stop people from going out. Anyone is free to leave the City anytime they want to. Once you leave, however, you are never supposed to return. So, no one ever does go out -- unless, of course, they are Exiled.
It was a fluke that I should have found the secret entrance. After safety, reliability was next most important to the Founders. What they built, they built to last for as long as possible. So it was sheer dumb luck that the annual test of the emergency ventilation system should fail on my watch. Ironically, it was their lack of regular use which caused the servo-mechanisms to fail. I couldn't believe my luck when they decided to replace all of them, and to make the job my responsibility. Of course, while I was making the replacements in the fab lab, I was being monitored, and I worked at my deliberate, careful pace. I did the same with the first mechanism I replaced -- after all, this was a job that had never been done before, so they had no idea how long it was supposed to take.
Suddenly, I had months of freedom on my hands. A day of working in the fab lab, a day of installing mechanisms, and I had finished my allotment for the week. Of course, I couldn't leave the unmonitored ventilation system for an area that was monitored, but it connected up with the entire City, and it was large enough for me to crawl through surprisingly easily.
It was the middle of the third week when I found the exit. It was large enough for me to walk through. A large fan stood in the middle of the passageway, but it was only switched on for the annual tests -- or in case of an emergency, if we ever had one. Normally a door hinged at the top kept the pasage closed, but it swung open when the fan was on. Propping it open was not a problem.
That's when I encountered my second bit of luck. The opening to the outside was 20 feet above the ground. There was screening to keep insects out, but I guess they felt that height was a sufficient deterrent. However, in the meantime a large tree had grown up next to it. It was a simple matter to remove the screen and climb down. Finally, I could explore the world outside the City.
Part 3: Outside