So you have a couple of skeins of Noro Kureyon and you want to make a striped hat.
Vertical or horizontal stripes?
How about both?

This pattern is incredibly easy—nothing more than knits, purls, and slipped stitches, with just one color used per row—but the end result will make even experienced knitters do a double-take: like magic, vertical stripes appear on one side of the fabric, and horizontal stripes on the other. The effects are accentuated by the use of two contrasting self-striping yarns.

Either vertical or horizontal stripes will show for most of the body of this reversible hat, and stripes running the other way appear when you fold up the brim. The decreases are worked in such a way as to be nearly invisible on both sides.

The pattern includes instructions for a scarf, cowl, and hat: the scarf and cowl are suitable for beginners, but the hat
decreases are worked over a large number of stitches and require more concentration and pattern-reading skills, and may be more suitable for an intermediate-level knitter.

This is the Ravelry entry for the hat, but instructions for all three accessories come as part of the pattern.