I figured out a simple method to draw good-looking hexgrids for pen-and-paper games. The trick is to draw a triangle grid instead. The only difference is that you'll have to play in the intersections. For good-looking grids, make sure the side of a triangle is 1.2 times the height.
Maximum A4 grid
At a comfortable grid size of 24mm per hex, an A4 sheet can fit 12x9 hexes, including the corners.
11x11 grid
At a slightly smaller 18mm grid size, an A4 can even accomodate a Hex board.
I used Inkscape to draw these grids, but it should be easy enough with a pen and straightline.
