Is it possible to create a magnetic environment where it pushes and pulls at the same time, making the target “levitate”? To better understand why I ask this, the backstory is I’m getting more and more annoyed by rolling office chairs rotating, hitting my ankles, hard to switch directions when wheels having ~90 degrees differences.
Imagine a ball, and put a bowl on it (upside down). The ball is metal, and the bowl is a magnet that pushes the ball, so it doesn’t touch it (because of the shape), and pulls it at the same time, so if you lift the bowl up the ball goes with it. This used as wheelchair castors could prevent my, and possibly others’ ankles to be hit.
Is it possible to create this environment that the magnets are in perfect balance in every direction, both pushing and pulling?
 A: I believe I have heard that there is a train in Japan which is supported by magnetic levitation, but that would be for linear motion, and might require a significant amount of power.
A: You can create a spatial array of magnets which generates a specific spatial force profile against a corresponding magnet array.
Check out polymagnets:
https://vimeo.com/107166551

Spring Polymagnets attract until they pass through a defined transition point, passed which they will repel. These Polymagnets will come to rest at an equilibrium distance.

I don't know whether it'd work for your specific spherical application though. I think it'd be easier to just redesign the normal wheelchair.
A: 
Is it possible to create this environment that the magnets are in
perfect balance in every direction, both pushing and pulling?

If by magnets you mean fixed magnetic moments in a static configuration, then the answer is no per Eanrshaw's theorem.
If the magnets are electromagnets or at least can change their magnetic fields dynamically, then maybe something can be done. With gravity you can build systems that are pull out of the ground (a metallic surface) due to induction while gravity pushes them down.
Another possibility is to use superconductors. With the right material and magnet, you can have a magnet that is locked at a certain distance from a superconductor (it can go up or down) due to flux pinning. Of course, this would only work at very low temperatures.
