I like the hat pattern in Last Minute Knitted Gifts. It's totally basic, but lets you customize ribbing or roll brim, ear flaps, pom poms, etc. the easiest version is roll brim: cast on, knit for a while, decrease, BO. You can make it fancy by adding fancy stitches, cables, etc if you're looking for a challenge, ot just add stripes, whatever! I don't think it would work for sz 15 needles.
Here's a basic pattern:
CO enough stitches to make a 20 inch circle that is a multiple of 6.
Join into a round
Knit all stitches around until hat measures 5-6 inches with the brim rolled.
K6, knit 2 together around
K5, k2tog around
K4, k tog around
K3, K 2tog
K, then run string through all left stitches, weave in end
you can decrease less for a less pointy top (or when you run out of stitches!)