Papa, lots if not most of us hike alone a great deal of the time. As long as yer not a dufus you'll be ok. 300winnmag (affectionately known as "slug dude), since he chose the name not me) points out the requirements.
Jim S oh and welcome. Will you have a 4wd vehicle? If so there are awesome places in the parks in Arizona, Zion, Bryce, Escalante, water fold etc, where you can get away from people. Just be aware that each different terrain/setting requires separate knowledge, that is - alpine, desert, etc.