Since other posters already suggested good ideas, I'd like to share one sort of "unorthodox" way of storing your mnemonic phrases.
Memorize it. Yes, you heard that right. A 12-word recovery seed is a lot easier to memorize that most people thought(though memorizing 24-word seed is still possible, just significantly harder). But I understand that this is definitely not for everyone.
And what if your Brain's memory is lost in an accident or something? That would mean no chance of ever recovering your phrase.
Writing them down somewhere remain the safest.