Why don’t the maps appear

The absolute best place to find SWEPS, Models, Maps, Tools, and Game Modes is garrysmod.org.

Posting this question/answer here, since the solution doesn't appear to exist anywhere else (outside of my own steam forums post):

Apparently Garry's Mod uses Internet Explorer somehow for its "FastDL" downloading. If Internet Explorer can't connect to the internet for whatever reason, then Garry's Mod won't download anything.

In my case, IE was set to offline-mode. Setting it to online fixed the issue.

Other things you can try:

• Make sure Options --> Multiplayer --> Download Custom Content is set to Allow All Custom Files From Server

• Try adding the following lines to the bottom of your garry's mod config file, located at Steam\steamapps\<username>\garrysmod\garrysmod\cfg\config.cfg:

  cl_allowdownload 1
  cl_downloadfilter all
  download_debug 0
  sv_downloadurl ""
  

• Verify the integrity of the game files. Within Steam: Library --> Garry's Mod --> Right Click --> Properties --> Local Files --> "Verify Integrity of Game Cache"

• Try disabling your firewall/antivirus, or possibly other non-essential programs/services running.

• Try deleting your maps, lua, addons, and cache folders in the garrysmod folder, located at Steam\steamapps\<username>\garrysmod\garrysmod. Then verify your cache again.

• As a last resort, uninstall Garry's Mod completely and delete the garrysmod folder (which you'll have to do by hand, because there will be leftover files), then reinstall.