Looking for where addons are downloaded in files

You can find the GMA (Garry's Mod Addon) located in a few places:

• addons on the Server and are named similar to ds_x.gma
  • garrysmod\cache\srcds may also have some named x.gma

You're probably looking for:

• garrysmod\downloads\server on the client side and are named x.gma

Keep in mind if you're looking for certain addon that x is the steam workshop addon ID found after the ID parameter for example: steamcommunity.com/sharedfiles/filedetails/?id=123123 is 123123.gma

Also, sometimes the files will be compressed and you'll need to extract them using an archive program like 7 Zip.

If you want to you can download the addons from a site, I suggest: http://steamworkshopdownloader.io/

If you already have the files you can try GMoshUI: https://github.com/FPtje/gmosh (this also helps to publish addons to the Steam)