National Park
You encounter Suicune for the first time outside the entrance to the National Park area on Route 36 in the center of Johto. You can either approach from Goldenrod City on Route 35 to the south and pass through the park, or approach from Violet City to the east. Suicune will run away before you can approach it.
Mt. Mortar
Your second encounter with Suicune is outside Mt. Mortar in the north of Johto. Suicune is outside the middle entrance to the mountain's caves, which you can access either by Route 42 from the west of Route 43. Again Suicune will run away before you can get near it.
Cianwood City
Suicune appears for the third time in Cianwood City to the southwest of Johto. If you head to the far north of town to the Pokemon Seer's house, you will find Suicune on the ledge to the right of the house. Once again it will flee before you can battle it.
Tin Tower
The final encounter with Suicune takes place at the Tin Tower in Ecruteak City, but before you go there, you must have completed the mission to clear Team Rocket from the Radio Tower in Goldenrod City. The Radio Director will give you a Clear Bell item as a reward, which you can use in the Tin Tower to stop Suicune from fleeing. Suicune is a Level 40 water-type Pokemon, and is weak against Electric and Grass-type moves.