Thanks to the World Gazetteer, the azimuthal map can now display world cities. The database has over 150,000 entries.
The azimuthal map form can now add labels for US cities. The database of latitude/longitude pairs for cities seems imprecise because some California cities are in the Pacific ocean. It might also mean that the coastal outlines are not precise enough.
If you notice a city out of place, please let me know. There are some errors in the database. For example, San Francisco was a few miles out to sea.
Update: I updated the list of cities to include ones from Alaska and Hawaii.