In the City State of the Invincible Overlord it is known as the Thieves' Quarter, in Lankhmar it is the Interlopers' Quarter, in Vornheim it is the Sixth District, in The City In The Waste it is the Fugitive Quarter, in Greyhawk it is The Intermittent Quarter, in Ptolus it is Quiettown, in Sharn it is Greyedge, in Orthrist it is The Neophytes, in Budapest it is Csigavaros, it is The Quarter On the Far Side Of The Corner, the Quarter Underneath.
If you have a living PC anywhere in all of D&D, Rolemaster, Warhammer, LOTFP, Pendragon or any other game like that, they have a home in the Snail Quarter. They may not want it, but there it is.
(this map totally bit and adapted from the City State of the Invincible Overlord)
To find your PC's home just click that picture and search by your own first and last initial. So if you're Dwight Eisenhower, your PCs live over the northwest corner of the Sword-Rat Resthouse. Why do we not go by the PC's name?
Because this way GMs can find you: If you want to find out who lives over the Assassin's Guild, find a C.K. and ask.
If your grid position indicates a home in the middle of a street or courtyard, that means your characters' apartments are inside one of the many bridges arching across the streets in the area.
1st and 2nd level PCs generally live on the second floor--after that, the higher the level, the higher the apartment.
Practically speaking, you can do whatever you want to your PC's room--just write the tag #SnailQuarter when you put it on the web to it so people can find it, see what kind of furniture, loot, or traps you keep there.
If you need a populated city district, there you go--just ask your friends who is where. If you are friends with Madonna or Darlene or Moebius or someone else with only one name, treat them as someone whose first and last initial are the same letter.
Over at grid Z/S, in a tower connecting the buildings along the Street on the Margins to the city wall-- Gorgut the Weasel (elf 1), Hellwheel the Moon-Slinker (wizard 1) and their ward, Slovenly Trull (half orc fighter 1) share an uncomfortable suite of rooms down the hall from warring zealots--Oculus the Unquiet (cleric 1), and Xorth the Insinuator (cleric 1)--on the second floor while, six floors above, it is rumored that Baron Blixa von Apfelsaft (thief 7) keeps a war elephant, a flailceratops and a xortoise. It would, at least, explain the noise.
If you want to meet Mordenkainen, I hear he's over the Dewy Dryad, and it is said Conan keeps rooms high above the locksmith on the Old South Road.