Welcome to Cerberus.
Make sure you do an Outpost run for dunes. http://wiki.ffxiclopedia.org/wiki/Outpost_Teleportation
Then go back to your home nation and find Easy Prey - Decent Challenge and xp till you hit 15 (with your party invite flag up).
At that point you can go to G-12 Konschtat Highland and kill worms (Rock Eater). This should take you till 17-18 safely.
If those are too easy you can try the worms in the Maze of Shakhrami or Korroloka Tunnels. Or if you have the WotG expansion head to N. Gustaberg (S)and kill those rock eaters.
The trick to killing worms is to cast as far away from the worm while running out of range when the worm tries to cast magic on you. Just be aware their range is longer than your own. Worms don't move from their spot which is why this works well. Be sure to bring some Selbina milk which can be found in Selbina (town in V. Dunes) for HP Regen. Make sure they are always claimed (red name) so they don't reset their hp.
This guide should help you past 20. http://wiki.ffxiclopedia.org/wiki/Black_Mage_Solo_Guide_by_Lion_heart
Oh yeah if you didnt know about the xp rings here is some info on that. This will greatly speed up your level gain. http://wiki.ffxiclopedia.org/wiki/Empress_Band