My neighbor listens to The Postal Service, likes to run, and hails from Wisconsin. Other than that, as far I know, he has no other interests or qualities. That's often how neighbors work. Unless you know your neighbors personally, you probably know very little about them. That is, if you even know their names. So what to give to these mystery people? Give them something you yourself would enjoy owning that's useful, and suggests you actually know something about these people, even though you don't. Be sure to write something to the effect of "I thought of you when I saw this because . . ." and then finish with a generic phrase.
Or, take the one thing you do know about this person, and run with it. For the guy who walks his Daschund by your house each morning, this pillow is a good choice. I've rounded up several items at various price points that will be sure to please that nice person next door.