Last year, we had a bear spotted in town, and one mountain lion.
This year, it's been a little more prevelent. A mountain lion was found dead, just South of town. One was spotted on the East side of town. One was heard on the North West side of town (growled at a lady walking her dog.) And now, one has been spotted on the West side of town in my yard.

It growled at my neighbor this morning but she didn't see it.
The mountain lion heard on the North West side, may be the same one that was spotted on the West side of town. Same creek runs along and it could be using that to wander back and forth.
We used to have an elk bugle about a block from my house. He was over in the creek bed almost every evening.
Suprisingly, I've never seen a coyote in town. Have seen them a ways out and I've heard them in town, but you know how their yap can carry.
Last year, I took my grandson fishing on the LittleHorn. We fished and walked and fished and walked. I was pointing out tracks in the snow of raccoons and stuff. When we walked back to the pickup, he said, "Grandpa, look." He pointed at a set of cat tracks (mountain lion) that were overtop of ours. He had followed us up the canyon. We never saw him, but his tracks were there.
Usually a cat won't attack you unless cornered or if you appear to be a deer. You know, dressed in tan or brown. But if you dress brightly you're usually fine. They'll follow you because they are curious.