If the earth is flat, then the horizon angle is exactly 90 degrees. That is, if you stand straight, and keep your eyesight perpendicular to your body's axis, then you'll see the horizon.
Since the earth is not flat, but a sphere, you would have to look slightly downwards to see the horizon.
In what kind of world would you have to look slightly upwards to see the horizon? I thought a bit and realized that the one-sheet hyperboloid would do it. However, it is not homogeneous like the plane or the sphere. After thinking a bit, I think it is impossible to find any homogeneous 2d surface in 3d Euclidean space that has the property.
So here's the question: in what kind of homogeneous 3d space* does there exist a homogeneous 2d subspace, such that its horizon has to be looked upwards?
I suspect it should be constructable from the spacetime geometry of a spherical gravity field, since in that world, if you are standing on a spherical shell centered in the field, light would bend downwards, and you'd have to look up in order to see the horizon.
* a 3-dimensional Riemannian manifold, such that its isometry group acts transitively on its oriented orthonormal frame bundle
For a relatively small 2-manifold in a relatively large 3-space there appears to be no solution. We may take the path of a light ray to be a geodetic or geodesic in the 3-space. The position of the horizon is therefore judged relative to such geodesics. A smooth homogeneous space is locally Euclidean, which means that all relatively small 2-manifolds will show horizons similar to when in Euclidean space proper.
However there are some intriguing variations on the conditions to be explored. I once read an SF comic in which the hero woke up in an alien valley and when he tried to walk out of it he eventually came back to where he had started. Turned out he was on the inside of a rotating toroidal space station and the "horizon" ahead and behind him was just the edge of the inner surface above his head.