How close a radius is the display? Within how many feet normally?

Welcome to the Apple Community.

That's a question that has no answer.

It depends on the connections that you have at the time. In some circumstances find my phone will allow me to determine which room in the house it is in, in other locations where it is connecting to different equipment, it may estimate by location to several miles.

The display is rectangular, not circular, hence talking about a radius is not appropriate.

It's to do with were you are not what you are using.