There are unfortunately not many options to tile a 2-dimensional plane with regular polygons. If you want to use only one kind of tile, then you can use squares or hexagons. You can use triangles, but then you have up-facing triangles and down-facing triangles. And that's it, because any other tiling schemes require weird combinations of many different tiles with different numbers of edges, which is going to end in a confusing mess. So unless you want those confusing and unnatural tiling schemes be the main gimmick of your game, I would really recommend against them.

So there are really no good options besides squares or hexagons.

If you use a square grid, then you can fix the problem of diagonal moves being cheaper than orthogonal moves by making diagonal moves cost \$\sqrt2\$ (1.414) times as much. Which you can approximate pretty well while still keeping the numbers as small integers when you make orthogonal moves cost 2 points and diagonal moves cost 3 points.

And then there is of course also the out-of-the box option: Do not use a grid at all! Just let units travel arbitrary floating-point distances up to their maximum movement in any direction they want, and resolve collisions by checking for geometric collider intersection. There are not many video games trying this. The only one I can think of is the 2004 game Phantom Brave. But it is rather popular in tabletop wargames like Warhammer (both 40k and Fantasy) and there are also people playing Dungeons and Dragons combat that way.

There are unfortunately not many options to tile a 2-dimensional plane with regular polygons. If you want to use only one kind of tile, then you can use squares or hexagons. You can use triangles, but then you have up-facing triangles and down-facing triangles. And that's it, because any other tiling schemes require weird combinations of many different tiles with different, shapes, sizes or numbers of edges. Which is going to end in a confusing mess. So unless you want those confusing and unnatural tiling schemes be the main gimmick of your game, I would really recommend against them.

So there are really no good options besides squares or hexagons.

If you use a square grid, then you can fix the problem of diagonal moves being cheaper than orthogonal moves by making diagonal moves cost \$\sqrt2\$ (1.414) times as much. Which you can approximate pretty well while still keeping the numbers as small integers when you make orthogonal moves cost 2 points and diagonal moves cost 3 points.

And then there is of course also the out-of-the box option: Do not use tiles at all! Just let units travel arbitrary floating-point distances up to their maximum movement in any direction they want, and resolve collisions by checking for geometric collider intersection. There are not many turn-based video games which try this. The only one I can think of is the 2004 game Phantom Brave. But it is rather popular in tabletop wargames like Warhammer (both 40k and Fantasy). Some people also play Dungeons and Dragons that way.