Buy cheap HQ items for leves turn ins, if you have those available. Same thing for GC turn ins.
Without crafting anything, you can get yourself to say...61 to use the cheap white crafting/gathering gear.
Case in point, leveled gsm from 66 to 70 in 15 min, with HQ ingots at 2k a pop, with about 30-40 leves. (can't remember exactly)
- Prices later went up to 12.5k an ingot though
If gear is up to date, success rates should be around 80% for gathering same level items I think.
Scrip items is also an excellent source of exp, when you run out of leves or turn ins.
Also tried the Moogle crafting quests?