This question concerns the post-crisis/New52 incarnation of the character.
Batman as a hero tries to hide in the shadows as much as possible (at least in the beginning, before becoming a more public figure) and reduce the amount of harm that will be done to him.
As such, he dresses mostly in black, or grey which can be hidden with the black of his cape. At one point, when sporting the yellow chest symbol, it was rationalized that this helps draw fire to the most reinforced part of his suit. But what about his utility belt?
The groing/stomach area is a dangerous area to target, and no rationalization was given for this. Indeed, many alternate costume do have the belt being black (such as the upcoming BvS movie) or a dark bronze instead of bright yellow (Arkham city) both of which make a lot more sense.
I understand that practically, in the real world it is a stylistic design choice, but I'm wondering if there is any in-universe explanation or rationalization, as it seems a very odd choice for the character to choose yellow instead of black or grey when his goal is to be stealthy.