It's kind of late in the game, but I found that you can get awesome ability points in the underwater dungeon where the fourth tablet is.
Every encounter there gives 6 ABP a shot and they're really easy monsters to kill (Except precious few). Also, theres a room in there with a high encounter rate where all you fight is a single enemy. (Some kind of fighter). You can knock him out in 3 hits easy, and then you get 5 ABP. (Note: For the record, this enemy uses Build-Up like a monk. You gotta get in those attacks before he hits your for 5000 damage, but you should be able to handle that.) I just walked around and got about a hundred ABP in a little over 5 minutes (Which ain't too bad).
A lot easier than Bal castle, and you don't have to worry about Lv.5 Doom running out.

Also, though I didn't hang there much, the underwater cave in the second world, that takes you to where you can find the single female chocobo and Shoat, there's monsters that provide 4 or 5 ABP there.

Also, in the beginning, at the Pirate ship, There are enemies who give 2 ABP in most encounters and there is a common encounter with 2 golems where you can receive 3 ABP. These sound like low numbers compared to what you can get at the very end of the game, but, in the beginning, when you only need 10-45 ABP to get into heavy class leveling, it's pretty good. And once you get up a few levels, the monsters are very easy to defeat. I pretty much went and leveled there when I wanted to level between the levels of 7 and 18, and I probably made 10 times the ABP because the battles were faster, they provided more ABP per, and they were easier. And IF you do get hurt there, the room is right next to four beds (Like a free inn) and a save point. It's an awesome spot in the beginning. Especially if you want to get everybody those key skills right away (Lv. 3 White & Black magic, BothHand, Brawl, Passages etc...)

If I find anything else, I'll let you know, but I doubt I will because I'm entering N-Zone. Maybe I'm forgetting something, but it really is hard to find groups of monsters that provide high ABP points early in the game. The monsters in the late Dungeons already give at least 4 ABP per fight, and it's only going to get higher. But there's no point, really, in doing research now. The high ABP rated in N-Zone are simply for helping you reach maximum strength before the final battle (Which is far too kind of the programmers, but I ain't complaining).