Probably the same thing Batman does, save people and stop crime. Not really much point in doing anything else, otherwise you'd just ruin the idea of Batman, who is the man. Pretty much one of the best heros of the Justice League. And he's effing intelligent as well.
I'd probably go around to random people and say in a deep voice: "I'm Batman." Then disappear, right as they turn around, JUST to piss them off....
*video is related. Watch it. Funnies sheitt*