Next step was to get libchamplain working so that the location data can be shown on a map. That turned out to be pretty easy. I found the easiest way was to do a git clone of their current repository. Doing that also meant that I could look at some of the example code, especially the python bindings they have with that library.

git clone git://git.gnome.org/libchamplain
./autogen.sh
./configure
make
sudo make install

I found launcher-gtk.py particularly helpful in understanding how the map drawing works.

If you prefer to just install the binaries, then this should do the trick:

sudo yum install libchamplain-devel libchamplain-gtk-devel libchamplain-demos

With both GeoClue2 and libchamplain installed, I now had enough information to get started on my mini-project to get my current (IP-based) location plotted. The code for this can be found here.