For day trips I brew coffee at home and carry it in a vacuum insulated bottle. The bottle smells like coffee even after cleaning, so I have one that I always use for the task.

For multi-day trips I already have a small camping stove (MSR PocketRocket or an alcohol stove), and I pack instant coffee. I heavily prioritize saving weight on longer trips, so I generally drink my coffee out of the same light plastic bowl that I just ate oatmeal out of, which doubles as a decent way to clean the bowl.