Lake Verity

At the beginning of the game, you hear rumors about The "Red Gyarados" being at lake Verity. Being the Pokémon nature, you naturally have to go check it out, and you meet up with your rival, and you guys go to the lake. There is nothing special there, except a few patches of grass, with a brief case sitting on it, which you guys stumble upon, and Bidoofs or Starlys attack you. In fear, you take the Pokémon out of the brief case, and like all the games, your rival gets the one with advantage over you.

Later on, after the Team Galactic incident, where you battle one of the Galactic leaders, you do a few things in the game, then you can meet the Pokémon Mesprit there, where it shows the picture for Dex purposes, then runs to the grasses of Sinnoh where you then have to find it to capture it.