All answers so far assume a system of orthogonal directions, each having an "anti direction". I suspect this predisposition is connected to our left-right symmetric bodies with natural forwards and backwards, as well as ups and downs. Languages constructed for aliens need not conform to this!
Take a starfish, for instance. If they have five distinct arms, that would give five directions in their plane, along with up and down.
For radially symmetric, disk-shaped creatures (or for communicating between radially symmetric spaceships or other vehicles) the only meaningful purely self-relative directions would likely be relative up and relative down (along with hither and away). For a creature shaped like a jellyfish, without any visual clues to other fixed directions, this could be combined with cardinal up and down.
Star or disk shaped creatures could of course point, either by turning their up or down towards something (which would be two different prepositions!), or by deforming themselves, shining a light etc. They could also use auxiliary phrases as "towards Alice" or "the way we came".
A more sophisticated option would also be to talk of the direction perpendicular to cardinal up AND to relative up, maybe like a cross product in mathematics? This would be sort of akin to our left and right, if the creature moves in its relative up direction, that is.