Similar to the Pravoka enemy area in the first game, FF2 has a place where high-level monsters roam near a town early in the game, resulting in massive death (and XP gain).

From the game's starting point in Altair, head directly South (down) until you hit the very end of the peninsula. The end of the peninsula is 1x3 squares, and by walking on the peninsula, one will encounter very powerful enemies early on in the game.

Some of the monsters encountered on FFII's point of peril:

Black Flan
Red Mousse
Killer Mantis
Behemoth (VERY rare)
Cockatrice
Adamantoise

Please note that you should not take on these enemies until everyone in your party has at least 300 HP, and until one member of your party has got their Fire, Ice, and Thunder spells to at least level 4.

Fighting these enemies this early on in the game is an excellent way to earn gil (each battle typically yields around 700-1500 gil) or to bring up your party's stats (though brining up your party's stats might be tough if you can't survive one hit). Some handy spells to have while fighting these enemies are Protect, Shell, Blink, and Berserk when you have more powerful weapons, and of course the three basic elementals.