At home, I have a separate book, but as I travel often, I also have a separate small travel notebook. Even this I cannot always access, which doesn’t matter: writing a to do list is about structuring your day at the start of it. You don’t need a beautiful book to get back to, or even re read it; you’ll remember.
In a little A6 notebook where I also write my plan for the day and any things that pop up. I carry it around everywhere with me.
I write my to-do list on my chalk board for home activities and in my notebook for work activities. Online to-do lists and apps don't worth me me as much as i would like them to.