Some good places to grind CP

According to the strategy guide, you can find Chichu in the Archlyte Steppe -??? AF-. In order to get its crystal, you need the Improved Moogle Throw fragment skill. If you have it, throw Mog into a patch of red flowers on the Plains of Eternity.

Because the Chichu monster crystal is one of a few only found using Mog, you don't fight it, so you could theoretically be any level as long as you have the improved Moogle Throw (which you get with the Mog's Manifestation fragment) and access to the Archlyte Steppe -??? AF-.

Flanitor has one great thing about him - of all the medics he learns Esunaga (Esuna on all) on the lowest level. Also, his Feral Link truly is a lifesaver. If you are about to be flattened, use his Feral Link, and when you are on full hitpoints he will cheer himself up so he can use it.

Flanitor is great but listen to this. You want Flanitor for the early Esuna. You also want the catigipillar (sp) who is the only monster in the game that learns elemental resist +30%. and it also learns raise real early so if you get it while your Flanitor is a low level, quickly level him up until he get eleresist and raise then infuse it into Flanitor. Then when Flanitor reaches level 34 and learns Esunaga (most of the game should be done by this point) infuse the Flanitor into a Green Chocobo for the single greatest medic in the world. Just infuse your Cait Sith with your Flanitor.