You can have an interesting idea “any” time. Problem is you may not even realize that you just had an interesting idea when you had it.
The journal is an excellent idea. I write everything down. When I look it over later, I’m usually embarrassed that I could have thought of anything so lame. But every once in a while, there are a few gems in there.
I always have pencil and a small notebook next to the bed. The best time for me to get good ideas is as soon as I wake up. The second best time is right before I go to sleep. I carry index cards and a pen at all times during the day, just in case.
The other important ingredient in good ideas is to get out there and experience things. All the time. You never know which inputs will spawn ideas, so get lots of inputs.
My best ideas have usually come when I see how something is and think, “There must be a better way.” Then I let it lie dormant inside and trust my “inner self” to come up with something when I least expect it.
(My best hacking ideas ever came from the first time I saw a code generator. Simultaneously I thought, “That is so cool!” and “It can be so much better than that.”)