Cities seem like the easiest challenge to tackle. Amazon could work with commercial and residential high rises and put a dock on their rooftops. So, the drone approaches the building rooftop, puts the package in the docking area (that keeps out poor weather), and then flies away. One of the receptionists could then get a notification of a new package, pick it up, and either put it in the appropriate mailbox, or hold it at the desk.
Want to get more advanced and efficient? When your package is delivered, Amazon sends you an access key to the dock. You can now go to the rooftop, type in your access key, and get access to the room to get your package. After it's claimed, your access key expires. This means only people with packages inside the dock have access. Yes, technically if you get a package delivered, you could access the room, and steal a package from someone else. However, there would likely be a camera in the room, and there's a record of you having access, so I can't see it being an issue. You could offset the risk even more by having 10 compartments in the docking area, so there's a 10x less chance of someone else having access to the same compartment. Right now I walk through my modern condo and see packages sitting in front of doors, in hallways without cameras, and there isn't a problem.
There might be 1,000 people living in a high rise, or thousands working in one. It would be easy to get tens of thousands of people access to air deliveries at home and work with a dozen docks. It's also a great selling point for offices and condos. "Our building allows you to receive air deliveries."