Obviously, Batman works best at night, where he can use stealth and intimidation to their maximum advantage. For a lot of fans, the idea of Batman going out during the day reminds them of the garish 1940s-1950s Dick Sprang era, or of Adam West.
But... I think that Batman is a driven enough character, focused enough on justice and protecting people that he would go out in the daytime if he needed to. For example, if the Joker took a bunch of hostages at a restaurant during the noontime rush, Batman wouldn't wait until sundown to deal with the issue, he'd be over there as soon as he heard about it.
What do you guys think?
Yes, I think a person as obsessed with fighting crime as Batman would definitely go out in the daytime to fight crime. Plus, whe he's with the JLA, I'm sure they fight crime during the day. Batman is too obsessed to limit his crime-fighting activities to night-time.