Is there a way to change the default Airdrop location from the Downloads folder to something else? I have changed the location of many other applications, so I assume it's possible, even is possibly taking a few lines in terminal.
Not easily, but you could enable Folder Actions on the Downloads folder before entering AirDrop and achieve the same effect on a more manual and case by case basis. It sure doesn't seem worth the set up unless you could somehow automate the whole sequence and were to use it many times.
In practice it might be easier to change the other programs like Mail and Safari to not use the same default Downloads folder that AirDrop does have hard coded as the save point.