Is there a way to select an area in GIMP, then fill every part of the selected that is a certain distance or more from the edges of the selection other than doing it manually?
So a black circle like this:
For one inner edge on any shape
- create a selection on your object (if you created the object with a selection you can reuse it)
- Select>To path
- Edit>Stroke path in "Line" mode. The width should be twice the one you want (one half is cut off by the selection).
If the object is on a transparent background this can also be done (a bit more accurately) using the
For several edges on arbitrary shapes
If it's arbitrary shapes, continue with the process above, selecting the inner shape. You may have to Select>Grow your selection by one pixel each time to avoid a tiny gap. The advantage of using a path to draw the border is that you can keep sharp angles (see the "Join" option in Stroke path), so your inner shape still looks like the outer one (otherwise the inner shapes will turn into an nondescript blob).
For concentric rings
If it is just plain rings, the good way is to stack decreasing rings. Position the center using two guides, and starting from this, create an Ellipse selection by forcing the aspect ratio to 1:1 and using the Expand from center option. In other words think of you image as this: