1. Bring on more of Batman's well known villains.
As much as I love Nolan's Batman series, one flaw I noticed was its lack of more well known villains. Sure, they included Joker, Two-Face, and even Scarecrow, but I think that, with TDKR being the last of Nolan's trilogy, I feel a bit disheartened that he didn't include villains like Mr. Freeze (if anyone can redeem him, it would be Nolan), Penguin, and even Riddler. I'm glad he's bringing Catwoman and Bane in, though.
2. A sleeker Batmobile
I loved the use of the Tumbler in the Nolaniverse, but I like how Tim Burton's Batmobile had much more of a classic feel. For the reboot, I would like to see a cross between the two, having an aggressive look but at the same time look like classic Batman.
3. The batsuit
Nolan's design on the Batsuit was absolutely perfect, except it was obviously not a clear adaptation straight from the comics. Burton's Batsuit was pretty good, with the use of the classic Batlogo. Like with the Batmobile, I'd like to see a cross between the Batman Forever costume (I hate Forever, but the costume design for that was good) and Nolan's take, giving a classic feel but also much more mobile. As for the logo itself, bring back the yellow circle, but make the actual bat similar to that of the Arkham Asylum logo. Oh, and no Battits or Batcrotches please.
4. Keep the dark, gritty feel.
Batman is a dark character, and people can't misuse him as a Happy Meal toy (-coughI'mlookingatyouGeorgeClooneyandAdamWestcough-) that kids think he is. Same thing with The Joker, Two-Face, The Penguin, etc. Nolan had the feel right on, and especially perfected it in The Dark Knight. I wouldn't ask for a duplicated feel for a reboot, but keep something that pays homage to what came before it.
5. Johnny Depp playing The Riddler
There isn't much to say about this one.
So yeah, there's what I've been thinking of what should be in the inevitable Batman re-reboot. If you have any suggestions, leave them in the comments below!