Hello, I downloaded Square and it works great but under reports I only have 2 options- Sales and Deposits.... I don't have a drawer option so how do I close out a drawer?

In your App go to settings and turn on Cash Management.  Then you will see it in your report menu.  This is only going to help you balance your cash in the drawer.  There is nothing that needs to be done to close the day.  

I have looked multiple times at the app menus, drilled down on every option, and I do NOT have this setting in the menu, even under cash drawers (only for electronic ones apparently). It WAS in the location everyone is saying, but is NOT there now. Any help deeply appreciated!

If you are using the Square Point of Sale app on your phone this option is not available because you cannot connect a drawer to the phone app.  You must use the tablet version to do that.