One issue with the sandbox campaign style is how much to build up front - the DM can quickly find themselves over preparing, and that's one of the most common recommendations to new DM's building a sandbox - start small, add on to it organically. With that in mind, there will be areas on the map that are ready for adventuring, and some areas that are stubs or left blank for future development.
A common technique Gary Gygax used in his dungeons was to wall off areas for this future development. Back in the early Greyhawk campaign of the 70's, Gary used "The Greyhawk Construction Company" - literally sawhorses, construction signs, orcs with hard-hats, etc, that let the party know the stuff down that hall or stairs was still being built, please come back later.
I'm going to use a less tongue-in-cheek approach for the Black City - higher level areas will be warded with automated guards like Watchers (from the bestiary article). If a Watcher is near a door or entrance, it'll be really hard to get past - lower level groups can't take on a stone golem (even an immobile one). By controlling access to the right colored gemstone passkeys, I can place sealed areas fairly early in the campaign, knowing the PCs can discover them when they're low level, but space beyond will remain a mystery until later in the campaign.
The following five areas on the surface map of the city (F Central Command, B Tower of Astronomy, O Institute of the Arcane, P The Plaza, Q Spire of Thaumaturgy) are all still-standing buildings that are inaccessible because of Watchers and other guards blocking access. They were hardened, shielded, and built to survive devastation, and a few of them still tower above the surrounding rubble. Players won't be able to access them until they've spent sufficient time acquiring enough of the right gemstone passkeys to avoid getting pulped by the Watchers at the entrance. However, these sealed buildings *will* be accessible from below, in the dungeons, when the party gets deep enough.
I'll post some notes on those five areas as the week goes on. Bit by bit, I'm working my way down the Black City project outline!