Not sure why, but after rolling back to 2.2.1 and then updating once more to 2.2.2, the locations are now appearing.
Strangely, the settings page looks different now. Before, there were a few input boxes for the Sandbox API displaying, almost as if Sandbox mode was enabled, even though it was unchecked. Perhaps it was enabled on a local version of the site and that changed a setting somewhere? Regardless, it seems to be working now.
UPDATE: After rolling back to 2.2.1, locations are successfully being fetched. Any idea what changed in 2.2.2 to cause this?