Well, it's good, but it's missing a main feature of most Batcaves, that being more platforms at different heights.
For example, those three pillars are really asking for a platform to be put on top of them.
While it appears that the elevator is the main entrance/exit, having ladders and platforms really helps sell the 3-D aspect of the Batcave. (Going up and down, and not just sideways.)
While the design is good, if you changed out the dark gray for light bley, then it would simply look like a fancy warehouse/bunker. Which is fine, if that is the look you're going for.
On the other hand, if you're going for a 2-D warehouse like his bunker from TDK then it's good, and doesn't need any work. (Well, the one dark gray LURP near the elevator kinda sticks out.) But it'll need some revision if you're going for a more traditional Batcave look.
Is there a reason it's shown to be built one brick above the baseplate? (Bottom left corner, top pic)
The drop seems kinda odd, and could be easily concealed. But being open like that, it's not really serving any decorative purpose that I can see. If it was the end of a large platform, the drop should be higher, if it's the floor, why not just keep everything more-or-less level?
I do like it overall. The SNOT plates on the back wall, as well as the Dark Gray rock parts, help to add some texture to it.
The top building is little more than Medieval Market Village with boarded up windows, so I'd say work on that before doing anything to the cave. It's not a bad look, just not very original.
Still, I'm looking forward to this! Keep up the good work!
P.S. Do you want me to keep reviewing your sets? I know they're not always glowing reports, so if you're sick of it, I'll stop.