Level 2 Key Spheres
As far as Level 2 Key Spheres go the best place I've found to farm them is in Zanarkand Ruins off of Defender Z. The Defender Z mobs drop Level 2 Key Spheres as an uncommon drop and Level 3 Key Spheres as a rare drop. I strongly recommend stopping for a bit and farming in the Zanarkand Ruins primarily for these mobs. If you spend an hour or two in this location you'll get all the Level 2 and 3 Key Spheres you need for now.
Another piece of advice you may or may not know about is getting 'Overkill' on an enemy will get you double the rewards after the battle. You should try to always get an Overkill strike on a Defender Z for this reason. If you're having trouble killing them or getting an Overkill try using Auron's Armor Break
If you've already passed Zanarkand Ruins and have the Airship, Omega Ruins is the best location for you to farm level 2 and level 3 Key Spheres. The fastest way for you to acquire them is to just bribe the enemy that has them, which is listed below. If you need more information on bribing read the Wikia.
Monsters that drop level 2 Key Spheres:
Defender X (Calm Lands)
Tonberry (Cavern of the Stolen Fayth)
Defender Z (Zanarkand Ruins & Omega Ruins)
Varuna (Omega Ruins)
Monsters you can Bribe/Steal for Level 2 Key Spheres:
Behemoth (Mt Gagazet) roughly 460,000gil Bribe
Some locations you can find Level 2 Key Spheres:
Sanubia Desert: Central (Chest)
Calm Lands (Chest)
Cavern of the Stolen Fayth (Chest)
Calm Lands Chocobo Minigame 1st place prize