I'd like to draw some closed paths with offsets on their internal edges, and I want the internal edges of the offset bands to be feathered. The external edge would be hard, not feathered. Below is an example of the effect I want, from a National Geographic map. Each colored band is transparent, but also feathered. Is there some way to do this in Illustrator, or will I have to create the effect in Photoshop? I've experimented with opacity masking but that doesn't seem to work. Suggestions?
There is always
Effect > Stylize > Inner Glow if that works for you. It is a raster effect.
I would handle this with a Gradient Mesh placed above the country/region. And making the internal mesh points transparent. This ultimately provides nearly complete control over the inner "glow" and remains vector.
Now, to be fair, using a Gradient Mesh is more advanced and many users can struggle with them at first. It's not a feature users tend to "pick up instantly". There are many tutorials out there though.
I'm not, by any means, stating this is the "correct" method to use. This is merely how I would tackle the same issue.