A friend recently told me she no longer has to fix her hair, having lost it to chemotherapy. We're not close, but I care about her a lot, and wanted to make her a hat. One of my favorite patterns is Danny Oulette's Easy Head-Hugger Hat.
This is a bit too big, but I think it can be washed and blocked to a smaller size.
Despite the name "easy," the pattern has some tricky elements. I never have mastered the technique of grafting it together at the end, so there is a seam.
The pillbox/fez shape isn't to everyone's taste, but I think it will suit her. I hope she likes it. She's an amazing woman, and she's beat cancer before. I'm confident she can do it again.