This is my idea of a classic looking (nodding towards the comics), yet practical Batsuit (nodding towards the Nolanverse):
Where the Armor Plates are flatter, closer fitting and molding to the body, built-in with the underlying suit. With the armor being flatter, and connected to the underlying suit, it doesn't stand out as much and thus looks more like the classic suit, yet without being a costume. Armor plates and underlying mesh-like suit are gray, but not a super light gray, so that it doesn't stand out too much from the black cowl, gloves, and boot. Of course, he'd have a cape, I just didn't draw it in...
I actually like the TDK/TDKR cowl and neck armor (minus the actual nostril shape on the cowl). It's practical, easy to remove and put on, and looks cool imo, so I left that in there. And I gave him the signature white eyes. That's something that can be built into the cowl. It may make it hard for an actor to see out of, but in a way I think it's more menacing because you can't see his eyes.
EDIT: The second concept is the classic blue cowl one. But straight blue wouldn't look practical, so I made it kinda blue-gray/slate-ish. That way the blue doesn't stand out too much from the gray (although it means the cowl, cape, gloves and boots are lighter than their black variants).