How can I find what is using the rest of my drive?

I use Daisy Disk to keep tabs on what's using up space on my disks. Like @Hoshts and @Joonas have mentioned in their comments on another answer it's not free, but gorgeous and easy to understand. Money well spent, in my opinion, unless you're just looking for a one-time solution.

One thing to keep in mind - the Mac App Store version of Daisy Disk is sandboxed - which means only the files your user can read will be counted.

If you use the direct download version of the app (which will assume the license from the MAS version if you install both and run the direct version after launching the MAS version one time and quitting it.) - it can run as Administrator and show all the files for all users on your Mac.

My favourite tool for this is http://grandperspectiv.sourceforge.net/ which gives a great graphical representation of files.

In your particular case, I have encountered issues with smaller "Solid State Drives" like those used in earlier MacBook Air system, where the system does not completely free up filespace on the SSD when some things have been deleted - perhaps waiting for some background tasks to take care of it eventually. To give the process a kickstart so to speak, I have run /Applications/Utilities/Disk Utility.app and used the "Erase Free Space" and that has freed up a lot of room that was not visibly being used when looking at any of the "file space" tools.

The older MacBookAir (2012 and before) machines can have the SSD upgraded to something bigger. See for example: http://eshop.macsales.com/shop/SSD/OWC/Air-Retina