I'm unable to specify which Steam library I want to install MW3 to

One solution is to make a symbolic link (Windows only, similar to a shortcut) from your Steam folder on your SSD to your HDD.

In this case, you would want to make a symbolic link from C:\Program Files (x86)\Steam\steamapps\common\ to S:\SteamLibrary\.

  1. Make sure that the folder C:\Program Files (x86)\Steam\steamapps\Call of Duty Modern Warfare 3\ does not already exist. If it does already exist, move it (and it's contents) to S:\SteamLibrary\Call of Duty Modern Warfare 3\. (cut+paste)

  2. Open the console. In Windows 7, open the Start menu and type cmd into the search bar at the bottom and press Enter.

    • If restrictions are in place, you may need to open CMD as an administrator. Hold CTRL + SHIFT when opening CMD to run as administrator.
  3. Type (or copy+paste) in the following: (right-click with your mouse to paste in console)

    mklink /D "C:\Program Files (x86)\Steam\steamapps\Call of Duty Modern Warfare 3\" "S:\SteamLibrary\Call of Duty Modern Warfare 3\"
    

    and press Enter. This will create a symbolic link from your C: drive to your S: drive. The difference between this and a regular shortcut is that Windows will read this as an actual directory and follow it to the other hard drive.

  4. Install normally. So long as it installs to C:\Program Files (x86)\Steam\steamapps\Call of Duty Modern Warfare 3\ (the location that we just made the link point from, and Steam's default install location for that game), the files will be stored on your S: drive.

  5. Enjoy your free SSD space! :)

Feel free to do this with as many games or folders as you want! (or your whole steamapps folder)