WARNING: The following article contains spoilers for Legends of the Dark Knight #14 by Brandon Easton, Karl Mostert, David Baron, Becca Carey, on sale now.
A tentative alliance between Batman and Azrael revealed that the latter has his own version of the Batcave, complete with it's own supercomputer and themed vehicles. The former Batman was clearly inspired by his time working as the Dark Knight to build his own sanctuary from the turmoil of the city in which he now resides.
Batman traveled to Italy while tracking Ra's al Ghul and his League of Assassins. The Dark Knight Detective discovered that Ra's was on the hunt for the blood of Saint Januarius, believing that whatever property caused the dried blood to liquify could supercharge a Lazarus Pit, making Ra's practically unstoppable. Batman managed to acquire the vessel holding the blood, but this put him in Azrael's crosshairs, triggering a chase through the city before the two were cornered by Ra's, who had been using Batman as a way to acquire the blood without having to do the work.
Batman and Azrael, now both on the side of keeping the blood out of Ra's' hands, teamed up to escape his assassins. Azrael created an opening for them by destroying the boat they were on, allowing the two to take a tunnel beneath the Venetian canals that lead to Azrael's secret lair that he called the Sanctum. Azrael explained that Batman wasn't the only one who needed to get away from annoying conversations with his allies from time to time. This did not amuse Batman, but he didn't deny that it was one of the perks of having a Batcave.
Azrael's Sanctum had much more in common with the Batcave than simply being an area of isolation. A cursory glance over the room revealed that Azrael not only possessed a supercomputer similar to the Batcomputer, but also displays of regalia associated with the hero's iconography. Symbols of his faith and the order he serves as well as weaponry was on full display.
But that wasn't the end of what Azrael had to offer from the Sanctum. He was still an agent of the Order of St. Dumas. Any secret organization that can survive for centuries is bound to have deep pockets, a fact Azrael proudly displayed with the reveal of his own aquatic vehicle designed after his armor, similar to his mentor's bat-themed vehicles. But his comments reveal that despite the Sanctum being a place for Azrael to regroup, it is clearly on the Order's payroll.
There are too many similarities to the Batcave to discount the possibility that Azrael might have been inspired by it. His time as Batman most likely made him realize that a home base with access to advanced equipment not only gave him a place to retreat, but also a means of achieving his goals when fieldwork wasn't cutting it. Indeed, Azrael's sanctum was key to providing him and Batman the means they needed to prevent Ra's' assassins from blowing up a historical site.
But Azrael isn't a wealthy man. The money most likely came from the Order he serves, meaning that his Sanctum isn't so isolated. But in a strange way that makes it more similar to the Batcave than dissimilar. Azrael joked that Batman only had one to get away from his allies, but most of them are aware of the Batcave's location and can drop in anytime. Azrael's allies are less trustworthy than Batman's though and might one day use this knowledge of his Sanctum to their advantage.