Every waking day I send tons of screenshots from my iPhone to my Mac via AirDrop. And every day I wish that Apple allowed users to customize the AirDrop save location. Not only is the ~/Downloads folder the default save location, but it can't be modified, not even via undocumented methods.
As a workaround, I use Hazel ($29 w/ free trial) to automate the process of moving images sent via AirDrop to my Desktop. It's a great workaround that does the job. While it would be nice if Apple allowed you to specify an exact save location, this is probably the next best thing.