Fincher and Aronofsky would have been great, but they are both at a point in their career where a franchise like this would be a 'burden' on them, which makes me think they just wouldn't put their heart and soul into it.
Alfonso Cuaron would be great for a more creative take on Batman, and he might just need a hit after the stumbles he's had with Gravity. Children of Men is brilliant and if he can infuse some of that style with Batman we'd be in for a treat.
Bennett Miller (director of Moneyball and Capote) hasn't done action yet, but damn those Moneyball baseball scenes were tense. He can tell an excellent story - I'd really like to see a less-predictable choice like him. Plus he is friends with Philip Seymour Hoffman - this could be a great casting choice for a villain (Penguin?). Then again, he might be great for a Daredevil reboot...
Brad Bird has been transitioning to live action. If there's one man who knows how to give gravitas to even the most superficially silly things (rats in kitchens, red spandex), it is this guy. Ghost Protocol was great.
Rian Johnson could be a great contender, but I'll hold off my official judgement until I see Looper. His other work, while niche, is great. He could do noir well - and it's been a dream of mine to see a great film-noir style Batman.