If you want to REALLY have a good shot at hunting a cat, you need well trained cat dogs, plain and simple.
If you like to go for a hike with a rifle; you might wind up seeing one someday. But LVSteve is onto something; you will take an awful lot more dogs, fox and bobcats than you will the big cat. They are VERY smart.
If I were going to try and find one without a set of dogs, I would look near canyons which have buzzards marking a kill. Go see if you can find cat tracks anywhere around the perimeter of the kill.
The cat will not be back for a day to 3 days, so be prepared to sit for a while. If you get up on a kill, it's pretty easy to tell if a cat or a dog is the culprit. Cats will drag their catch off the path and half bury it or kind of stash it. Dogs just tear into it right where they kill it.
If you stink up a cat kill, get ready to kill dogs; the cat WILL wind you, and will never return.
A friend tracks them in Texas a lot; they run a cycle of about 30 days in a given area. They cover tremendous ground; they move as far as elk, not like deer.
Every sense on the cat is superior to the senses of all their wild counterparts. Better eyes than dogs. A nose that beats deer, equals hogs. Their 'spider-sense' tingles all day long; they sense things being out of place like a marine DI raiding a barracks at 3am. Their hearing is nothing short of spectacular.
If you want to know where I have seen 3 of the 4 big cats I have seen in the wild??? In BACK of me, and every one was about 20 yards away. Each time, I turned to look back for something, and there was mister Kittums, stalking me, or just happening to be walking behind me. I do think one of them was as surprised as I was; he had the look of 'WHAT in the world are YOU doing here??!!' And then he rocketed off. One decided to walk toward me; I kicked up dust and started yelling. He just backed away and left. The last one glared at me, then his look went to that of- of all things, a CAT. It looked all harmless, and 'nice kitty' and walked away.
That one creeped me out the most.
Of the 3 cats who stalked me, 2 of the 3 were where I was hiking going fishing; no gun on me at all. The 3rd one was where we hunt quail, I was scouting the area looking at the hatch and broods of chicks. Again; no gun.
Have only seen 1 while out hunting. About 1,300 yards thru my spotting scope. Have no idea if he realized I was there. Watched it for about a minute, and it disappeared.
Wishing you good luck.
...well not that i know of 
