From the top of my head, I like the 7pm music the best. It's so soothing somehow. I know there are really pretty tunes during the night as well, but I'm not really good at staying up late so I haven't had the chance to experience them in-game yet.
My favorite's definitely 1 AM, to the point that it's actually my favorite song in the entire game. It's just so calming and atmospheric. Not to mention it really goes well with rain, and I love rain.
The runner ups are 7 PM and 11 PM, for similar reasons to 1 AM.
Mine would be more of a dislike of one hour: 7 to 8 pm. I cannot STAND that music. There is just something about it that I find sinister. It touched off some kind of childhood fear and I never come on during that hour. If I have to, I keep the sound turned down. Weird? Yes. But that's just me, lol.
I like 6am, although I never play it then, lol. It's upbeat, yet it's calming. If you wake up that early, it's be a great thing to sort of get you going.