The problem there is you're thinking in 3d space. The surface of a sphere is two dimensional, a two dimensional creature living there would be able to travel in a straight line in any direction and they'd end up back where they started; they have no concept of "up" or "down" so wouldn't be able to move up to leave the surface of the sphere.
A 4d sphere would be similar; the surface of that sphere is three dimensional. A three dimensional creature (like a human) could travel in any direction along the surface of that sphere and end up back where they started, they would have no concept of "into" or "out of" that sphere so wouldn't be able to leave it.
A picture of a hypersphere is trying to represent a 4d object in two dimensions, you lose a lot of data every time you lose a dimension.