I'm trying to install Emmet via Package Control in Sublime Text 3 but whenever I search for it it just doesn't show up.
Any ideas? Am I missing a repository maybe?
It may be that you've already installed Emmet. First, go to Preferences -> Package Settings and see if there's an Emmet submenu there. Alternatively, Preferences -> Package Settings -> Package Control -> Settings-User has a list of all installed packages. Finally, you can check your Installed Packages folder for an Emmet.sublime-package file - go to Preferences -> Browse Packages... to open your Packages directory, navigate one level up, and Installed Packages should be right there.
If you find Emmet at one of those locations, but for some reason it's not working for you, go to Preferences -> Package Control to open up that section of the Command Palette, select Package Control: Remove Package, then type in emmet and hit Enter to remove it. You should then be able to select Package Control: Install Package from the Command Palette and pick Emmet from the list.