Hi and welcome to Knitting Help!
Knitting Fool is such a great site, Claire. Here's more choices, some less elastic than others (scroll down to ribbing).
Nicky Epstein has a section on various ribbing alternatives in her "Knitting on the Edge" and "Knitting Over the Edge". Both of these are available at my library and maybe at yours, too.
I found this right before Christmas time. I made three matching Packer hats for my son in law, daughter, and granddaughter. The ribbing on this is k2,p2, but the design itself is amazing. This hat is easy to do, looks great, and is one of the few that fit your head nicely. My daughter commented that for some reason, the yarn felt softer with this pattern. Try one and see what you think. They knit up quickly.
There's a lot of them out there that make interesting hats. The one in the pattern link I gave you is a knit 6, p2 rib. I've also seen k 5, p1. K3, p1. K3,p2. One of my favorites is for a rib stitch that lies flat and won't stretch. This is the Twin Rib stitch. It looks the same on both sides. It's cast on in multiples of 3. First row: k3, p3 across row. Second row: k1, p1 across row. Another one of my favorites is a thermal stitch. This is cast on in a multiple of 4. It's knit one row, purl one row. Knit 2, purl 2 for two rows. Repeat these four rows for pattern. It looks like the waffle pattern on long underwear. It's extremely warm. But I'll warn you. I did a blanket like this for my granddaughter when she was first born and the blanket is extremely heavy weight wise with this stitch.
fatoldladyinpjs said:"Another one of my favorites is a thermal stitch. This is cast on in a multiple of 4. It's knit one row, purl one row. Knit 2, purl 2 for two rows. Repeat these four rows for pattern."
I used this stitch pattern to knit my grandson in VA a scarf to go with his hat and gloves I knitted for his Christmas present. . He loved them.
Daylilies are the Lord's smiles, a new one every day.