Idk if you will ever need this, but if you like hexagonal grids that are rotated 30degrees you can have almost perfect one with vertices that lie on integer coordinates: just build a hex from triangle (0,0), (11,11), (15, -4). This is due to the fact that 2*(11^2)=242~ 241=15^2+4^2 and (7,4) vector being very close to 30 degrees. Alternatively, just build flat top hexes out of (0,0), (4,7), (8, 0)