I would have preferred him to have been fighting in the early morning
The scene is early morning in Gotham. Catwoman is riding off at dawn on the bat-pod and she doesn't blow the hole in the covered up highway tunnel until the early morning when the battle starts.
At first I had reservations about Batman being out in day light. But in context of the story, it made sense. When you think of Batman out during the day you naturally think of the whimsical and goofy 60's series.
But it makes sense. In BEGINS he established this mythic creature mostly at night. Nolan and Bruce treat him as a dracula and true Bat like creature in the first two films. Only bringing him out with hints of sunlight at dusk or dawn, but mostly at night.
So by the time TDK Rises comes along, Batman has a cemented legend and threat among everyone in Gotham. Everyone respects him. The only reason he comes out in the day is to lead the good of Gotham in "war" to reclaim their city. And by all accounts, he's still intimidating even in day light. That is a testement to the manner in which the character was written, Bale's tense physical precense, and the beautifully constructed paramilitary esque TDK suit which looks intimidating and practical even in harsh lightings like day light or brightly lit interrogation rooms.
Plus Gotham's streets weren't populated by civilians. It was Dent's criminals, mercenaries, and cops ... all people who are well aware of the Batman's capabilities, whether they fear or respect him.
It makes sense thematically that it come full circle and Batman brings the dawn to Gotham.