Suicune is the only Pokémon you'll see running wild around Johto. You don't have to chase Suicuine everywhere, because Suicune will only appear at specific locations.

	The first spot is the one and only, Burnt Tower. It has changed after a year from Gold/Silver. Awaken the legendary Pokémon and watch as Suicune gets left behind, only to look at you for a few seconds.
	The second spot is at the top of Cianwood City. After it runs away, you'll be challenged by a trainer named Eusine, who is looking for Suicune to train by himself. He has Drowzee Lv. 23, Haunter Lv. 23, and Electrode Lv. 25.
	The Third spot is near the three Apricorn trees in front of Mount Motar. Use Cut, and watch as Suicune runs away once again.
	The Fourth spot is beneath a Berry Tree in Route 32, after the National Park. Then Suicune will flee towards the Tin Tower.
	You won't be able to meet Suicune anymore, unless you get by the Wise Trio in the Tin Tower. Get the clear bell after saving the Radio Tower from Team Rocket, and deafeat the Wise Trio to have the chance to capture Suicune.
	After defeating the Wise Trio, enter the second tower and meet Suicune, along with Raikou and Entei. The two will flee, but Suicune will stay, and you'll get the chance to capture a brand new Suicune!