Hiking in the mountains is my favorite thing in the world. I mostly hike in British Columbia in the summer. The Selkirk Mountains, the Rocky Mountains, that area, but I've hiked in Arizona as well, and a few other places. Mostly I hike on trail, but sometimes I go off trail. Sometimes there's an easy route where there's no actual trail. Some of my most fun hikes have been (for me) very difficult off-trail hikes.
However, I almost never hike alone, and when I do hike alone I stay in very familiar and very easy terrain. Since none of my friends hike, this means I go to hiking lodges where guides are provided as part of the package, or I hire a private guide. I prefer a private guide because then we hike at my pace, so I often hire a private guide even at a lodge. Hiking alone is more dangerous than hiking with other people because if something goes wrong (twisted ankle, e.g.) you've got help. But I know that some people really find inner peace hiking alone.
I presume you know what you are doing and are properly prepared for your hike. I hope you enjoy it as much as I think you will. The mountains are so soothing, so calming, and the exercise is so much fun.
P.S. My avatar is a picture of me on a steep slope with fixed ropes. There's some exposure, which makes it scary, but it's loads of fun. Most of the hike is trail, but this one section is just a route with ropes fixed in place.