Since I constantly have a hard time when in lower levels in finding a good place to grind. I have found some info on the massive Internets on the best places to Fate Grind depending on level.

1-10 Class quests, hunting log completion, fates in the area around your hunting log as they pop up. Goes fast on secondary classes thanks to Armory XP buff. Don't forget to use your Chocobo battle buddy! Especially helpful when killing monsters on your hunting log that are higher level than you.
10-20 Aleport, Western La Noscea
20-30 Quarrymill, South Shroud
30-35 Costa del Sol, Eastern La Noscea
35-45 Dragonhead, Coerthas
45-50 Ceruleum Processing Plant, Northern Thanalaan

Please view the levels listed above as a simple guide. It's not particularly difficult to get into a party in Costa around level 28. Just be aware that you will take hard hits that you're not used to. :)

Enjoy.