It's convenient to think about this in an inertial frame of reference. Imagine yourself floating in absolutely empty space, without any force acting on you.
Now add a rotating cylinder somewhere. Did anything change? If you ignore the mass of the cylinder (probably it's small) and atmosphere, there is no reason your floating state should change.
If the atmosphere rotates together with the cylinder (a reasonable assumption), you will feel no wind if you are in the center, and stronger wind if you are near the edge. The absence of wind is the only reason you could call it "floating zone" in the center, but not near the edges.
Now imagine a thrown ball (ignore the atmosphere for simplicity). It's moving in a straight line; if it passes through the center, it should reach a wall in future.
As for how you could return to the center if you are at the edge: you could climb a pole (or a rope, or the cylinder's wall at one of its ends) that reaches to the center. While climbing, you would feel a weak Coriolis force, but it would be small compared to the artificial gravity.
I have now realized that this description is incomplete without considering what the wind will do to you. Floating at the center is an unstable state. At any point except the center the wind will push you in the direction of cylinder's rotation, and if you are denser than air, you will tend to continue in a straight line, coming closer to the wall ("falling"). In your new position, the wind is stronger, and you will "fall" faster, so at the end you will crash into the wall.
The theory behind this is described in this Wikipedia article.