I used the magic of Google Maps Street View to see what it's like over there. It doesn't look particularly sinister. (Actually I think Chris Monti lives in that general neighborhood -- shhh!)
No word on whether anything was still in the back seat (the guitar and Christmas presents). I didn't ask about the trunk because I don't really want anyone new poking around in there.
I get to pick it up tomorrow any time after 9 am. (This is ideal, because it means I get to take at least one medium-sized trip in the good old rental car before I have to return it.) Does anyone feel like giving me a ride? (Time flexible.) The address of the tow lot is 754 Branch Avenue.
Thanks to everyone for their encouragement and kind thoughts.
I guess I should call my insurance company.
Edit: I called up my insurance guy to let him know, and he confirmed what I suspected, which is that 'undamaged' doesn't necessarily mean, for instance, 'drivable'. So we will see. Still, I'm just happy they found it so fast.