It would be nice if they made Bruce's main entrance to the Batcave from the house be through a large grandfather clock, with the clock being the lock with a combination. The combination would be the exact time at which the Waynes were killed. In the comics, that was 10:47, I believe.
Obviously they have to put in an advanced computer with access to multiple restricted databases, or it simply isn't the Batcave, which means it's not really the Batman. You can get away with no computer for the first movie, but that's it.
I'd actually like it if they put in a few "Bat-poles," meaning just poles to slide down. Anyone who thinks that would be "corny" or "cheesy" is an unforgivable idiot, and to even be listened to, they would also have to think it was cheesy for
firemen to use those poles. You know, like they do in
real life in emergencies? Anyway, having multiple entrances to the Batcave from within the house is a good idea, and the poles would be the one-way entrances to use when things are especially urgent. I would also be perfectly fine with giving them elevating platforms, possibly CO2 powered, that can get him back up the poles, but I think there are too many fans insecure and ashamed of their interest in superheroes that would protest to protect their egos due to "cheesiness" or whatever excuse, and I can live without it.
If they really wanted to make it a true Batcave, they'd give him a CSI lab. I realize Nolan isn't really into the whole "detective" thing (yes, that's meant to be as derisive as it sounds), so that's probably too much to hope for.
There should be an emergency medical station down in the cave. There's absolutely no excuse for not having one after the first movie. Not every affliction can be fixed by calling up the friendly basement-dwelling scientist and getting an antidote. Also, since this version of the Batman is so unconfident of his chances of avoiding gunfire through evasive movement as to weigh himself down with a bulky suit impractical for his line of work, he'd better have a surgical station ready in case someone uses ammo that can break through his puffy robot costume, or shoots him in the face, or something. They should also make it clear that Alfred was a military field medic.
If they wanted to cover even more of the real Batman's character and arsenal of tactics, they'd also have a corner of the cave with an actor's dressing room type nook and wardrobe. This would be where the Batman creates and reuses disguises with makeup and prosthetics as well as costumes, to walk the streets looking like a civilian or criminal instead of the Batman or Bruce Wayne. That would be another chance to show off the Batman's cleverness.