I quit caffeine a couple of different times by carefully measuring my intake and reducing it by a tiny amount every week. I was methodical about it, and my brain didn't notice the change from one week to the next.
That is currently my goal, but I'm in love with the boost I get in the morning from coffee. I quickly go from groggy to fully alert. Most Americans do the same thing.
When I wasn't consuming caffeine, just drinking liquid in the morning helped me get started.
Coffee is beneficial to health because of antioxidants, but we can get antioxidants from other sources.