I've never heard of "General Delivery" either. I'd be afraid it would end up someplace I wouldn't be able to find it!
I have had the same experience as Camoprincess with PO Boxes though. If the package doesn't fit, they get put in a locker in the lobby, and the key to the locker is inside my PO Box.
I believe you can also rent a box at a UPS Store, and those provide you with an actual street address rather than just a PO Box.