I use the Battle Arena, especially the fight against that stupidly dangerous uber-cactuar creature thing.

Here's what you need:
Weapons with Overdrive->AP ability on everyone (and, preferably, Triple Overdrive too)
'Comrade' overdrive mode
Spells like Auto-life and Hastega

Basically, fight the cactuar-ish monster whose name I forget, give everyone Auto-Life, and let it go nuts on your party. That fiend deals between 9999 and 99,999 damage with every hit - and he hits a lot. 'Comrade' means that everyone's Overdrive gauge will fill as their friends take damage, and Overdrive->AP means that their Overdrive gauge will automatically be changed into AP. Keep everyone alive, and after a couple of minutes the entire team will have gained 99 Sphere levels - the maximum possible for one fight. Then you simply have to dispatch the fiend, save your game, and repeat till your heart's content.

Getting a weapon with Triple Overdrive and Overdrive->AP isn't always easy, but the bonus items won from Battle Arena challenges and from getting every Al Bhed Primer (then talking to Rin) can help things along well.