Sometimes fixing a blown out part of a pictures using an adjustment brush or radial filter just doesn't get you what you need without a lot of work. Sometimes they catch things in the foreground that is exposed correctly and getting the masking right can take a lot of work. If you shoot raw there may be a simpler way of recovering the detail. Works to recover both blown out and under exposed parts of a picture.

When I know I'll have some exposure problem with something being too overexposed or underexposed I use auto exposure bracketing and then merge the shots in post via Lightroom's Photo Merge - HDR feature into a single much better exposed picture. If you shoot raw you can do the same thing if you only have a single copy of the picture by using virtual copies, making broad adjustments and then merging the copies.

Here is a "final" product I needed to fix:

The background behind the arch is too blown out to look good. Since people were constantly moving the normal auto exposure bracket and merge wouldn't work because the people would have moved between shots. While Lightroom can handle this I didn't want to tempt fate. I tried post processing using an adjustment brush but didn't feel like doing the hard work of working around the trees and lamp post in the foreground.

So I went back to the original import and made a virtual copy:

I created a virtual copy of that picture and adjusted the exposure -1.65 to get this:

Then I used the HDR merge of the two versions to get this:

That gave me a much better overall exposure and the background details were now visible. I went back to the original black and white and copied all the settings I used to create it and pasted those on the new image to get a much better-looking version of the original.

I spent less than five minutes doing things this way while it probably would have taken me thirty minutes or more with adjustment brushes.