Okay so the Abyss from that one japanese mango, huh. Well, you probably don't need to map out the first two levels, but even then it's good to have a good idea of the hub's general layout
>Fortifications, nearby farms, sources of water, merchant district, whatever the official ruler surrounds his HQ with (e.g. noble neighborhood), slums, ghettos, industrial districts for the trading hub's main exports, major places of worship, etc.
As far as I know, your players don't care about this stuff most of the time. Figuring out the details of a city is a way for you, the DM, to come up with cool ideas for encounters, set pieces, descriptions and plot points.
The third level has got to be some kind of catacombs, tunnels, or ruins from a previous city, maybe. You've got lots of potential dungeon structures here. You say the dungeon branches out into an underground city, a cavern, a path to the Underdark, a bigass monster's lair, and a flooded section. So we can infer a bunch of monsters already.
>CAVE and UNDERDANK: A variety of random Monstrosities and Beasts
>UNDERDANK-specific: Mind flayers, drow, myconids, duergar, all that jazz
>LICH CITY: The traditional undead roster, I probably don't need to list this here
>BIG BAD LAIR minions, pets, slaves, allies and charmed creatures
>In the case of a BEHOLDER: Some humanoid slaves, gas spores, other aberrations, lesser beholders (and if you want to get creative: nothics, golems, oozes...)
>In the case of a DRAGON: Kobolds, various humanoid slaves, cultists (and again, more out-there ideas: elementals related to dragon's color, mimics, living gem-encrusted weapons...)
>SPLASH MOUNTAIN OF DEATH: Probably kuo-toa, but hezrou coming out of a hellish rift deeper into the abyss would be kickass too.
Those monsters aren't staying in their homes. They're hunting, scavenging, being chased off, scouting or expanding their territory into the Main Dungeon. That's already a fuckload of potential encounters.