Where I am from in northern Idaho it is infested with Cougars and they come into town at night and kill dogs.Not many people hunt them because they are extremely elusive and rarely ever seen and seldom leave much sighn. They are mostly nocturnal and usualy sleep during the day.In my entire life I have seen five of them. If you are going to travel a lot of miles to see one I would suggest you contact a guide with dogs who can tree you one and be in good shape because you will be convering some rugged terrain.
Most are treed and shot with a 22 magnum. Your 243 is enough and then some, they are not hard to kill like a bear nor nearly as dangerous. They are usualy up high and feed off mule deer but ocasionly come down lower and kill white tails.You have picked a very hard to spot critter and are more than likely going to be disapointed unless you hire a guide chances are so very slim you will see one.