Can reminders have a custom location? Is it possible to move the location pin in the Reminders app, or otherwise set a custom location?  I want to set a reminder at a place with no address.

(This is on an iPhone 7, so 3D Touch is available.)
Introduction
The iOS Reminder application does not allow for free moving of the locator pin. The best you can get is entering the address of where to place it (logically), as most people want to be reminded when arriving at or leaving a pre-known location.

Potential Alternatives  


While it is not possible to move the pin around on the map, you may
find that you can physically get to the location ahead of time and
use the Remind at Current Location option to set future reminders.
Obviously, this depends on the distance between you and that
location, but if you use it frequently, you set up correctly once
don't worry about it again. This should be made easier with the next idea.
I would recommend that you use an app like Maps to get the exact
location that you require and extract the address from it. If it is
a public space or company, this is often enough of a locational
marker to import straight into the Reminders app. This would be my
go to method.


Conclusion
The native Reminders app does not allow you to move the locator pin but perhaps 3rd party apps do, however this is beyond the scope of your question. If you are looking for more ways to use the Reminders app for location-based reminders, take a look at this article from Apple.
I would be interested to know how you made out. Let me know.