I made this one for a 2 year old and a 3 year old. It it an inch of 2:2 ribbing, then 2 repeats of the lace pattern from the lace beanie on knitty, then stockinette. I think it came out cute, but not too cutesy.
There is also a free pattern for a cabled hat, where the cables look like owls. I can dig it up if you are interested. I also think the Kittyville Hat (also available for free) is cute.