The Monster Arena is one of the new additions to Dragon Quest 3 Remake from the original; here's how it works.
While you can level up anywhere in Dragon Quest 3 HD-2D Remake, the best places include Metal Slimes/Liquid Metal Slimes. They give you the most bang for your buck when it comes to leveling up.
The first time you can find Metal Slimes in Dragon Quest III: HD-2D Remake will most likely be on the fifth floor of the Tower of Transcendence, which is around the halfway point of the game.